Statistics CO
UNION CHRISTIAN COLLEGE, ALUVA
COURSE PLAN ( 2021 – 2022 )
Department  MATHEMATICS 
Name of Faculty  
Programme Name  B.Sc MATHS & B.Sc PHYSICS 
Level of study  UG 
Semester  FIRST 
Course Name/Subject Name  DESCRIPTIVE STATISTICS 
Total Hours  72 
Course Outcomes
CO Number  Description  CO Evaluation methods 
CO1  Define and use the basic terminology of statistics. To get them equipped with different statistical presentation of data. To explain the statistical concept of census and sampling. Analyse and compare different Sampling methods.  Assignment, Test 
CO2  Calculate and interpret the various measures of central tendency and dispersion. To get them equipped with different statistical presentation of data.  Assignment, Test 
CO3  To acquire the knowledge about the characteristics of a distribution such as moments, skewness and kurtosis.  Assignment, Test 
CO4  To understand the characteristics and properties of Index numbers.  Assignment, Test 
Module 1  Hours : 20  
Syllabus:
DIFFERENT ASPECTS OF DATA, AND ITS COLLECTION Statistics as collected facts and figures, and as a science for extracting information from data. Concepts of a statistical population and sample. Different types of characteristics and data qualitative and quantitative, cross sectional and timeseries, discrete and continuous, frequency and nonfrequency. Different types of scale nominal and ordinal, ratio and interval. Collection of datacensus and sampling. Different types of random samples simple random sample, systematic, stratified and cluster sampling. 

Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO1  Statistics as collected facts and figures, and as a science for extracting information from data. Concepts of a statistical population and sample.  4  Lecture, PPT  
2  CO1  Different types of characteristics and data qualitative and quantitative, cross sectional and timeseries, discrete and continuous, frequency and nonfrequency.  6  Lecture, PPT  
3  CO1  Different types of scale nominal and ordinal, ratio and interval.  3  Lecture, PPT  
4  CO1  Collection of datacensus and sampling. Different types of random samples simple random sample, systematic, stratified and cluster sampling.

7  Lecture, PPT  
Module 2  Hours : 20  
Syllabus:
CENTRAL TENDENCY AND DISPERSION Averages Arithmetic Mean, Median, Mode, Geometric Mean, Harmonic Mean and Weighted averages. Absolute Measures of dispersion Range, Quartile Deviation, Mean Deviation and Standard Deviation. Combined mean and standard deviation, C.V, relative measures of dispersion, Ogives and Box plot.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO2  Averages Arithmetic Mean, Median, Mode, Geometric Mean, Harmonic Mean and Weighted averages.  8  Lecture, Problem solving  
2  CO2  Absolute Measures of dispersion Range, Quartile Deviation, Mean Deviation and Standard Deviation. Combined mean and standard deviation, C.V, relative measures of dispersion  10  Lecture, Problem solving  
3  CO2  Ogives and Box plot.  2  Lecture, PPT, Problem solving  
Module 3  Hours : 15  
Syllabus:
Moments, Skewness and Kurtosis Raw moments, central moments and their inter relations. Skewness Pearson’s, Bowly’s and moment measures of skewness. Kurtosis percentile and moment measure of kurtosis.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO3  Raw moments, central moments and their inter relations.  6  Lecture, Problem solving  
2  CO3  Skewness Pearson’s, Bowly’s and moment measures of skewness.  5  Lecture, Problem solving  
3  CO3  Kurtosis percentile and moment measure of kurtosis.  4  Lecture, Problem solving  
Module 4  Hours : 17  
Syllabus:
INDEX NUMBERS Definition of Index Numbers. Price Index Numbers. Price Index Numbers as Simple (A. M., G. M.) and Weighted averages (A. M.) of price relatives. Weighted averages (A. M.) of price. Laspeyer’s, Paasche’s and Fisher’s Index Numbers. TimeReversal and FactorReversal tests. Cost of living index numbersfamily budget and aggregate expenditure methods. An introduction to Whole sale Price Index and Consumer Price Index.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO4  Definition of Index Numbers. Price Index Numbers. Price Index Numbers as Simple (A. M., G. M.) and Weighted averages (A. M.) of price relatives.  5  Lecture, Problem solving  
2  CO4  Weighted averages (A. M.) of price. Laspeyer’s, Paasche’s and Fisher’s Index Numbers.  4  Lecture, Problem solving  
3  CO4  TimeReversal and FactorReversal tests.  4  Lecture, Problem solving  
4  CO4  Cost of living index numbersfamily budget and aggregate expenditure methods.  2  Lecture, Problem solving  
5  CO4  An introduction to Whole sale Price Index and Consumer Price Index.  2  Lecture, Problem solving  
Department  MATHEMATICS 
Name of Faculty  
Programme Name  B.Sc MATHS & B.Sc PHYSICS 
Level of study  UG 
Semester  SECOND 
Course Name/Subject Name  PROBABILITY THEORY 
Total Hours  72 
Course Outcomes
CO Number  Description  CO Evaluation methods 
CO1  Define the basic rules and concepts of probability. Solve the problems in probability.  Assignment, Test 
CO2  Explain the concepts of random variables. Differentiate the ideas between discrete and continuous random variables. Evaluation of conditional probabilities and unconditional probabilities. Solving problems using change of variables.  Assignment, Test 
CO3  Explain the concept of a twocomponent random vector. Analyse the bivariate random variable using p.d.f, c.d.f, marginal and conditional probability, independence.  Assignment, Test 
CO4  To understand the concept of scatter diagram. Differentiate the ideas between correlation and regression, Identification of regression lines.  Assignment, Test 
Module 1  Hours : 20  
Syllabus:
PROBABILITY Random experiments. Complement, union and intersection of events and their meaning, Mutually exclusive, equally likely and Independent events. Classical, frequency and Axiomatic approaches to probability. Monotone property, Addition theorem (up to 3 events) .Conditional probability. Multiplication theorem (up to 3 events). Independence of events. Baye’s theorem. 

Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO1  Random experiments. Complement, union and intersection of events and their meaning, Mutually exclusive, equally likely and Independent events.  5  Lecture, PPT, Problem solving  
2  CO1  Classical, frequency and Axiomatic approaches to probability.  4  Lecture, Problem solving  
3  CO1  Monotone property, Addition theorem (up to 3 events)  3  Lecture, PPT, Problem solving  
4  CO1  Conditional probability. Multiplication theorem (up to 3 events). Independence of events. Baye’s theorem.  8  Lecture, PPT, Problem solving  
Module 2  Hours : 17  
Syllabus:
PROBABILITY DISTRIBUTION OF UNIVARIATE RANDOM VARIABLES Concept of random variables. Discrete and continuous random variables. Probability mass and density functions and cumulative distribution functions. Evaluation of conditional probabilities. Evaluation of unconditional probabilities. Change of variables methods of Jacobian and cumulative distribution function (one variable case).


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO2  Concept of random variables. Discrete and continuous random variables.  2  Lecture, Problem solving  
2  CO2  Probability mass and density functions and cumulative distribution functions.  6  Lecture, Problem solving  
3  CO2  Evaluation of conditional probabilities. Evaluation of unconditional probabilities.  6  Lecture, Problem solving  
4 
CO2 
Change of variables methods of Jacobian and cumulative distribution function (one variable case).  3  Lecture, Problem solving  
Module 3  Hours : 15  
Syllabus:
PROBABILITY DISTRIBUTION OF BIVARIATE RANDOM VARIABLES Concept of a twocomponent random vector. Bivariate probability mass and density functions. Marginal and conditional distributions. Independence of Bivariate random variables.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO3  Concept of a twocomponent random vector.  2  Lecture, Problem solving  
2  CO3  Bivariate probability mass and density functions.  5  Lecture, Problem solving  
3  CO3  Marginal and conditional distributions.  5  Lecture, Problem solving  
4  CO3  Independence of Bivariate random variables.  3  Lecture, Problem solving  
Module 4  Hours : 20  
Syllabus:
CORRELATION AND REGRESSION Bivariate data types of correlation. Scatter diagram. Karl Pearson’s product moment and spearman’s rank correlations coefficients. Regression equations fitting of polynomial equations of degree one and two; exponential curve. Two types of regression curves, Identification of regression equations.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO4  Bivariate data types of correlation. Scatter diagram.  3  Lecture, PPT  
2  CO4  Karl Pearson’s product moment and spearman’s rank correlations coefficients.  5  Lecture, Problem solving  
3  CO4  Regression equations fitting of polynomial equations of degree one and two; exponential curve.  6  Lecture, Problem solving  
4  CO4  Two types of regression curves, Identification of regression equations.

6  Lecture, Problem solving  
Department  MATHEMATICS 
Name of Faculty  
Programme Name  B.Sc MATHS & B.Sc PHYSICS 
Level of study  UG 
Semester  THIRD 
Course Name/Subject Name  PROBABILITY DISTRIBUTIONS 
Total Hours  90 
Course Outcomes
CO Number  Description  CO Evaluation methods 
CO1  Explain the concept and illustrate the different aspects of mathematical expectation  Assignment, Test 
CO2  To understand the applications of discrete and continuous probability distributions in day to day life and to solve the problems.  Assignment, Test 
CO3  Describe the Chebychev’s inequality, Weak Law of Large Numbers and Bernoulli’s Law of Large Numbers and to explain Central Limit Theorem.  Assignment, Test 
CO4  Identify the different sampling distributions. Discuss their properties and relation among them.  Assignment, Test 
Module 1  Hours : 20  
Syllabus:Mathematical expectation
Expectation of random variables and their functions. Definition of – Raw moments, central moments and their interrelation, A.M, G.M, H.M, S.D, M.D., covariance, Pearson’s correlation coefficient in terms of expectation. MGF and characteristic function and simple properties. Moments from mgf. 

Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO1  Expectation of random variables and their functions.  4  Lecture, PPT, Problem solving  
2  CO1  Definition of – Raw moments, central moments and their interrelation, A.M, G.M, H.M, S.D, M.D., covariance, Pearson’s correlation coefficient in terms of expectation.  10  Lecture, PPT, Problem solving  
3  CO1  MGF and characteristic function and simple properties. Moments from mgf.  6  Lecture, PPT, Problem solving  
Module 2  Hours : 25  
Syllabus:Standard probability distributions
Uniform (discrete/continuous), Bernoulli, binomial, Poisson, Geometric, hypergeometric, exponential, gamma one and two parameter(s), beta (type I and type II) – mean, variance, mgf, additive property, lack of memory property. Normal distribution with all properties.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO2  Uniform (discrete/continuous), Bernoulli, binomial, Poisson, Geometric, hypergeometric, exponential, gamma one and two parameter(s), beta (type I and type II) – mean, variance, mgf, additive property, lack of memory property.  20  Lecture, PPT, Problem solving  
2  CO2  Normal distribution with all properties.  5  Lecture, PPT, Problem solving  
Module 3  Hours : 20  
Syllabus:Law of large numbers and central limit theorem
Chebychev’s inequality. Weak Law of Large Numbers Bernoulli’s and chebychev’s form. Central Limit Theorem (Lindberg Levy form with proof)


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO3  Chebychev’s inequality.  6  Lecture, PPT, Problem solving  
2  CO3  Weak Law of Large Numbers Bernoulli’s and chebychev’s form.  8  Lecture, PPT, Problem solving  
3  CO3  Central Limit Theorem (Lindberg Levy form with proof)  6  Lecture, PPT, Problem solving  
Module 4  Hours : 25  
Syllabus:Sampling distributions
Concept of sampling from a probability distribution. i.i.d observations. Concept of sampling distributions. Statistic(s) and standard error(s). Mean and variance of sample mean when sampling is from a finite population. Sampling distribution of mean and variance from Normal distribution. Chisquare distributions. Student’s t distribution. Snedecor’s F distribution and statistics following these distributions. Relation among Normal, Chisquare, t and F distributions.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO4  Concept of sampling from a probability distribution. i.i.d observations. Concept of sampling distributions. Statistic(s) and standard error(s).  7  Lecture, PPT, Problem solving  
2  CO4  Mean and variance of sample mean when sampling is from a finite population.  5  Lecture, PPT, Problem solving  
3  CO4  Sampling distribution of mean and variance from Normal distribution.  5  Lecture, PPT, Problem solving  
4  CO4  Chisquare distributions. Student’s t distribution. Snedecor’s F distribution and statistics following these distributions. Relation among Normal, Chisquare, t and F distributions.  8  Lecture, PPT, Problem solving  
Department  MATHEMATICS 
Name of Faculty  
Programme Name  B.Sc MATHS & B.Sc PHYSICS 
Level of study  UG 
Semester  FOURTH 
Course Name/Subject Name  STATISTICAL INFERENCE 
Total Hours  90 
Course Outcomes
CO Number  Description  CO Evaluation methods 
CO1  Explain the concept of estimation of parameters. Calculate the problems related to point estimation. To acquire the knowledge about the properties of good estimators.  Assignment, Test 
CO2  To discuss the methods of estimation and solve the problems related to interval estimation.  Assignment, Test 
CO3  Explain the concepts of Testing of Hypotheses. Hypothesize various advanced statistical techniques for modeling and exploring practical situations. Solve the problems related to Testing of Hypotheses (Large Sample Tests)  Assignment, Test 
CO4  Solve the problems related to Testing of Hypotheses (small sample test)  Assignment, Test 
Module 1  Hours : 25  
Syllabus:Point estimation
Concepts of Estimation, Estimators and Estimates. Point estimation and Interval estimation. Properties of good estimators; unbiasedness, Efficiency, Consistency and Sufficiency. Factorization theorem (statement).


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO1  Concepts of Estimation, Estimators and Estimates. Point estimation and Interval estimation.  10  Lecture, PPT, Problem solving  
2  CO1  Properties of good estimators; unbiasedness, Efficiency, Consistency and Sufficiency.  12  Lecture, PPT, Problem solving  
3  CO1  Factorization theorem  3  Lecture, PPT, Problem solving  
Module 2  Hours : 20  
Syllabus:Methods of estimation and interval estimation
Method of moments. Method of maximum likelihood. Invariance property of ML Estimators. Method of minimum variance. CramerRao inequality (statement only) confidence intervals for mean, variance and proportions.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO2  Method of moments. Method of maximum likelihood. Invariance property of ML Estimators. Method of minimum variance.  12  Lecture, PPT, Problem solving  
2  CO2  CramerRao inequality (statement only) confidence intervals for mean, variance and proportions.  8  Lecture, PPT, Problem solving  
Module 3  Hours : 25  
Syllabus:Testing of hypotheses, large sample tests
Statistical hypotheses, null and alternate hypotheses. Simple and composite hypotheses, TypeI and typeII errors. Critical Region. Size and power of a test, pvalue. NeymanPearson approach. Large sample tests – ztests for means, ztests for difference of means, ztests for proportion, ztests for difference of proportion. Chisquare tests for independence, homogeneity.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO3  Statistical hypotheses, null and alternate hypotheses. Simple and composite hypotheses  4  Lecture, PPT  
2  CO3  TypeI and typeII errors. Critical Region. Size and power of a test, pvalue.  5  Lecture, PPT, Problem solving  
3  CO3  Neyman – Pearson approach.  1  Lecture, PPT  
4  CO3  Large sample tests – ztests for means, difference of means  5  Lecture, PPT, Problem solving  
5  CO3  Large sample tests – proportion and difference of proportion  5  Lecture, PPT, Problem solving  
6  CO3  Chi – square tests for independence, homogeneity.  5  Lecture, PPT, Problem solving  
Module 4  Hours : 20  
Syllabus:Small sample tests
Normal tests for mean, (when o known). Normal tests for difference of means (when o known). Normal tests for proportion (when o known). ttests for means (when o unknown), ttests for difference of means (when o unknown), paired ttest ,test for proportion(binomial), chisquare test. Ftest for ratio of variances.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO4  Normal tests for mean, difference of means and proportion (when σ known)  6  Lecture, PPT, Problem solving  
2  CO4  ttests for mean and difference of means (when σ unknown)  4  Lecture, PPT, Problem solving  
3  CO4  paired ttest  2  Lecture, PPT, Problem solving  
4  CO4  test for proportion (binomial)  2  Lecture, PPT, Problem solving  
5  CO4  Chi – square test for variance, Ftest for ratio of variances.  6  Lecture, PPT, Problem solving  
Department  MATHEMATICS 
Name of Faculty  SWATHY K. N 
Programme Name  B.Sc PSYCHOLOGY 
Level of study  UG 
Semester  FIRST 
Course Name/Subject Name  BASIC STATISTICS 
Total Hours  55 
Course Outcomes
CO Number  Description  CO Evaluation methods 
CO1  To inculcate in students the need and importance of statistics in Psychology. Define and use the basic terminology of statistics. To get them equipped with different statistical presentation of data.  Assignment, Test 
CO2  To explain the statistical concept of census and sampling. Analyse and compare different Sampling methods.  Assignment, Test 
CO3  Calculate and interpret the various measures of central tendency.  Assignment, Test 
Module 1  Hours : 20  
Syllabus:
Introduction to StatisticsIntroduction to Statistics. Need and importance of Statistics in Psychology. Variables and attributes, Levels of Measurement: Nominal, Ordinal, Interval and Ratio. Collection of dataprimary and secondary, census and sampling, classification and tabulation, grouped and ungrouped frequency table. Diagrammatical and graphical representation of data bar diagram, pie diagram, frequency polygon and curve, histogram, ogives.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO1  Introduction to StatisticsIntroduction to Statistics. Need and importance of Statistics in Psychology.  3  Lecture, PPT  
2  CO1  Variables and attributes, Levels of Measurement: Nominal, Ordinal, Interval and Ratio.  3  Lecture, PPT  
3  CO1  Collection of dataprimary and secondary, census and sampling, classification and tabulation, grouped and ungrouped frequency table.  6  Lecture, PPT  
4  CO1  Diagrammatical and graphical representation of data bar diagram, pie diagram, frequency polygon and curve, histogram, ogives.  8  Lecture, PPT, Problem solving  
Module 2  Hours : 15  
Syllabus:
Census and Sampling. Different methods of sampling. Requisites of a good sampling method. Advantages of sampling methods. Simple random sampling, Stratified sampling. Systematic sampling.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO2  Census and Sampling. Different methods of sampling. Requisites of a good sampling method. Advantages of sampling methods.  8  Lecture, PPT  
2  CO2  Simple random sampling, Stratified sampling. Systematic sampling.  7  Lecture, PPT  
Module 3  Hours : 20  
Syllabus:
Measures of central tendencymean, median and mode properties, merits and Demerits.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO3  Measures of central tendency  2  Lecture, PPT  
2  CO3  Mean – properties, merits and Demerits  6  Lecture, Problem solving  
3  CO3  Median – properties, merits and Demerits.  6  Lecture, Problem solving  
4  CO4  Mode – properties, merits and Demerits.  6  Lecture, Problem solving  
Department  MATHEMATICS 
Name of Faculty  SWATHY K. N 
Programme Name  B.Sc PSYCHOLOGY 
Level of study  UG 
Semester  SECOND 
Course Name/Subject Name  STATISTICAL TOOLS 
Total Hours  54 
Course Outcomes
CO Number  Description  CO Evaluation methods 
CO1  Calculate and interpret the various measures of dispersion  Assignment, Test 
CO2  To acquire the knowledge about the characteristics of a distribution such as moments, skewness and kurtosis.  Assignment, Test 
CO3  To understand the concept of scatter diagram. Differentiate the ideas between correlation and regression, Identification of the regression lines.  Assignment, Test 
Module 1  Hours : 17  
Syllabus:
Measures of dispersionRange, quartile deviation, Mean deviation, standard deviationproperties, merits and demerits, coefficient of variation.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO1  Measures of dispersion  1  Lecture, PPT  
2  CO1  Range – properties, merits and demerits  3  Lecture, Problem solving  
3  CO1  Quartile deviation – properties, merits and demerits  4  Lecture, Problem solving  
4  CO1  Mean deviation – properties, merits and demerits  4  Lecture, Problem solving  
5  CO1

Standard deviation – properties, merits and demerits, coefficient of variation.

5  Lecture, Problem solving  
Module 2  Hours : 20  
Syllabus:
Raw Moments, Central Moments, Inter Relationships (First Four Moments), Skewness – Measures – Pearson, Bowley and Moment Measure, Kurtosis Measures of Kurtosis – Moment Measure.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO2  Raw Moments, Central Moments, Inter Relationships (First Four Moments)  8  Lecture, Problem solving  
2  CO2  Skewness – Measures – Pearson, Bowley and Moment Measure  7  Lecture, Problem solving  
3  CO2  Kurtosis Measures of Kurtosis – Moment Measure.

5  Lecture, Problem solving  
Module 3  Hours : 17  
Syllabus:
Karl Pearson’s Coefficient of Correlation, Scatter Diagram, Interpretation of Correlation Coefficient, Rank Correlation, Regression, Regression Equation, Identifying the Regression Lines.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO3  Scatter Diagram  2  Lecture, PPT  
2  CO3  Interpretation of Correlation Coefficient, Karl Pearson’s Coefficient of Correlation, Rank Correlation  7  Lecture, Problem solving  
3  CO3  Regression, Regression Equation, Identifying the Regression Lines.

8  Lecture, Problem solving  
Department  MATHEMATICS 
Name of Faculty  SWATHY K. N 
Programme Name  B.Sc PSYCHOLOGY 
Level of study  UG 
Semester  THIRD 
Course Name/Subject Name  PROBABILITY AND PROBABILITY DISTRIBUTIONS 
Total Hours  54 
Course Outcomes
CO Number  Description  CO Evaluation methods 
CO1  Define the basic rules and concepts of probability. Solve the problems in probability.  Assignment, Test 
CO2  Explain the concepts of random variables. Differentiate the ideas between discrete and continuous random variables. Analyse the discrete random variable using p.d.f, c.d.f, expectation, mean, variance  Assignment, Test 
CO3  To understand the applications of Binomial and Normal distributions in day to day life and psychological problems.  Assignment, Test 
Module 1  Hours : 17  
Syllabus:
Probability: Basic concepts, different approaches, conditional probability, independence, addition theorem, multiplication theorem (without proof) for two events, simple examples.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO1  Probability: Basic concepts  3  Lecture, PPT, Problem solving  
2  CO1  Different approaches  3  Lecture, PPT, Problem solving  
3  CO1  Addition theorem  1  Lecture, PPT, Problem solving  
4  CO1  Conditional probability, independence, Multiplication theorem (without proof) for two events  10  Lecture, PPT, Problem solving  
Module 2  Hours : 17  
Syllabus:
Random variables, Discrete and Continuous, p.m.f and p.d.f., c.d.f of discrete r.v. Mathematical Expectation of a discrete r.v, Mean and Variance of a discrete r.v.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO2  Random variables, Discrete and Continuous  1  Lecture, PPT  
2  CO2  p.m.f and p.d.f., c.d.f of discrete r.v  8  Lecture, Problem solving  
3  CO2  Mathematical Expectation of a discrete r.v, Mean and Variance of a discrete r.v.  8  Lecture, Problem solving  
Module 3  Hours : 20  
Syllabus:
Binomial distribution mean and variance, simple examples. Normal distribution definition, p.d.f, simple properties, calculation of probabilities using standard normal tables, simple problems.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO3  Binomial distribution mean and variance, simple examples.  8  Lecture, Problem solving  
2  CO3  Normal distribution definition, p.d.f, simple properties  2  Lecture, PPT  
3  CO3  Calculation of probabilities using standard normal tables, simple problems.  10  Lecture, Problem solving  
Department  MATHEMATICS 
Name of Faculty  SWATHY K. N 
Programme Name  B.Sc PSYCHOLOGY 
Level of study  UG 
Semester  FOURTH 
Course Name/Subject Name  STATISTICAL INFERENCE 
Total Hours  54 
Course Outcomes
CO Number  Description  CO Evaluation methods 
CO1  Explain the concepts of Testing of Hypotheses. Hypothesize various advanced statistical techniques for modelling and exploring practical situations.  Assignment, Test 
CO2  Solve the problems related to Testing of Hypotheses (Large Sample Tests)  Assignment, Test 
CO3  Solve the problems related to Testing of Hypotheses (small sample test)  Assignment, Test 
Module 1  Hours : 17  
Syllabus:
Testing of hypothesis Statistical hypothesis, Simple and composite hypothesis Null and Alternate hypothesis, Type I and Type II errors, Critical Region, Size of the test, P value.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO1  Testing of hypothesis Statistical hypothesis, Simple and composite hypothesis Null and Alternate hypothesis  8  Lecture, PPT  
2  CO1  Type I and Type II errors, Critical Region, Size of the test  8  Lecture, PPT, Problem solving  
3  CO1  P value.  1  Lecture, PPT, Problem solving  
Module 2  Hours : 17  
Syllabus:
Large sample tests – ztests for means, difference of means, proportion and difference of proportion, chisquare tests for independence, homogeneity. 

Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO2  Large sample tests – ztests for means, difference of means  6  Lecture, PPT, Problem solving  
2  CO2  Large sample tests – proportion and difference of proportion  6  Lecture, PPT, Problem solving  
3  CO2  Chi – square tests for independence, homogeneity.  5  Lecture, PPT, Problem solving  
Module 3  Hours : 20  
Syllabus:
Normal tests for mean, difference of means and proportion (when σ known), ttests for mean and difference of means (when σ unknown), paired ttest, test for proportion (binomial), chi – square test for variance, Ftest for ratio of variances.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO3  Normal tests for mean, difference of means and proportion (when σ known)  7  Lecture, PPT, Problem solving  
2  CO3  ttests for mean and difference of means (when σ unknown)  5  Lecture, PPT, Problem solving  
3  CO3  paired ttest  2  Lecture, PPT, Problem solving  
4  CO3  test for proportion (binomial)  2  Lecture, PPT, Problem solving  
5  CO3  Chi – square test for variance, Ftest for ratio of variances.  4  Lecture, PPT, Problem solving  
Department  MATHEMATICS 
Name of Faculty  
Programme Name  MA ECONOMICS 
Level of study  PG 
Semester  FIRST 
Course Name/Subject Name  Mathematical Methods for Economic Analysis 
Total Hours  90 
Course Outcomes
CO Number  Description  CO Evaluation methods 
CO1  This is a course on the basic mathematical methods necessary for understanding modern economics literature. Mathematics provides a logical, systematic framework within which quantitative relationships may be explored, and an objective picture of the reality may be generated. The deductive reasoning about social and economic phenomena naturally invites the use of mathematics. Among the social sciences, economics has been in a privileged position to respond to that invitation, since two of its central concepts, commodity, and price, are quantified in a unique manner. Thus, a good understanding of mathematics is indispensable for better cognizance of almost all fields of economics, both applied and theoretical. The goal of the course is to make students understand, assimilate and thus capable of using the mathematics required for studying economics at the master’s level. This course will focus on developing the mathematical tools that are used extensively in Microeconomics, Macroeconomics, and Econometrics. Students should be given an introduction to the Linear algebra, Differential Calculus, Integral Calculus, etc. These mathematical methods would help students in their understanding of advanced and core courses in Economics. The aim of this course is to: (i) introduce the students to several mathematical tools used in modern economics; (ii) illustrate the use of these tools by applying them to various wellknown economic models; and (iii) complement the core postgraduate microeconomic and macroeconomic theory courses. Learning outcomes: On completion of this unit, successful students should be able to demonstrate understanding of static optimization and dynamic systems applicable to economics.  Assignment, Test, Viva, Seminar 
Module 1  Hours : 15  
Syllabus:Linear algebra
Definitions of vector and matrix. Types of matrices, Addition, subtraction and multiplication of matrices. Determinants, Minors, Cofactors, Adjoint and Inverse of a matrix. Solution of a system of linear equations – Cramer’s rule and Inversion method. Rank of a matrix Linear independence of vectors. Some applications in Economics – Input output analysis – Partial equilibrium market model. 

Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO1  Definitions of vector and matrix. Types of matrices, Addition, subtraction and multiplication of matrices. Determinants, Minors, Cofactors, Adjoint and Inverse of a matrix.  5  Lecture, PPT, Problem solving  
2  CO1  Solution of a system of linear equations – Cramer’s rule and Inversion method.  4  Lecture, PPT, Problem solving  
3  CO1  Rank of a matrix Linear independence of vectors.  4  Lecture, PPT, Problem solving  
4  CO1  Some applications in Economics – Input output analysis – Partial equilibrium market model.  2  Lecture, PPT, Problem solving  
Module 2  Hours : 25  
Syllabus:Differential Calculus
Limit of a function – Derivative of a function. Rules of differentiation – Higher order derivatives – L’Hospital rule of finding the limit of a function. Differentiation of implicit function – Partial and total derivative of a function with several variables. Maxima and minima of a function. Curvature properties – Convexity and concavity – Points of inflection. Properties of homogeneous functions – Euler’s theorem. Matrix calculus: Rules of Matrix differentiation, differentiation of a matrix by a scalar, differentiation of a scalar by a matrix. Some applications in Economics Derivation of Marginal cost, Marginal revenue functions – Derivation of point elasticity, tax yield and income multiplier, problems relating to indifference curve and isoquant. Production function, utility functions, cost functions. CobbDouglas production function, CES production function – Comparative static analysis of market model, national income model, input output model, determination of partial elasticities of demand. 

Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO1  Limit of a function – Derivative of a function. Rules of differentiation – Higher order derivatives – L’Hospital rule of finding the limit of a function. Differentiation of implicit function – Partial and total derivative of a function with several variables. Maxima and minima of a function.  7  Lecture, PPT, Problem solving  
2  CO1  Curvature properties – Convexity and concavity – Points of inflection. Properties of homogeneous functions – Euler’s theorem.  5  Lecture, PPT, Problem solving  
3  CO1  Matrix calculus: Rules of Matrix differentiation, differentiation of a matrix by a scalar, differentiation of a scalar by a matrix.  5  Lecture, PPT, Problem solving  
4  CO1

Some applications in Economics Derivation of Marginal cost, Marginal revenue functions – Derivation of point elasticity, tax yield and income multiplier, problems relating to indifference curve and isoquant. Production function, utility functions, cost functions. CobbDouglas production function, CES production function – Comparative static analysis of market model, national income model, input output model, determination of partial elasticities of demand.  8  Lecture, PPT, Problem solving  
Module 3  Hours : 25  
Syllabus:Integral Calculus
Indefinite integrals – rules of integration, initial conditions and boundary conditions. Integration by substitution, Integration by parts – Integration of natural exponential functions. Definite integrals – properties of definite integrals. Area under a curve, area between curves. Difference equations and differential equations (basic concepts only). Improper integrals – Beta and Gamma integrals. Some applications in Economics – Consumer surplus and producer surplus – continuous interestdiscount calculation. Cobweb model, multiplier accelerator. Harrod – Domar and Solow model. 

Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO1  Indefinite integrals – rules of integration, initial conditions and boundary conditions. Integration by substitution, Integration by parts – Integration of natural exponential functions. Definite integrals – properties of definite integrals.  9  Lecture, PPT, Problem solving  
2  CO1  Area under a curve, area between curves. Difference equations and differential equations (basic concepts only). Improper integrals – Beta and Gamma integrals.  8  Lecture, PPT, Problem solving  
3  CO1  Some applications in Economics – Consumer surplus and producer surplus – continuous interestdiscount calculation. Cobweb model, multiplier accelerator. Harrod – Domar and Solow model.  8  Lecture, PPT, Problem solving  
Module 4  Hours : 25  
Syllabus: Linear Programming
Formulation of LPP and solution using graphical and Simplex methods. Duality theory – constrained optimization with inequality and nonnegativity constrains. KuhnTucker formulation. Primal and duel, shadow prices. Applications from Economics and Finance.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO1  Formulation of LPP and solution using graphical and Simplex methods.  7  Lecture, PPT, Problem solving  
2  CO1  Duality theory – constrained optimization with inequality and nonnegativity constrains.  7  Lecture, PPT, Problem solving  
3  CO1  Duality theory – constrained optimization with inequality and nonnegativity constrains.  7  Lecture, PPT, Problem solving  
4  CO1  Applications from Economics and Finance.  4  Lecture, PPT, Problem solving  
Department  MATHEMATICS 
Name of Faculty  
Programme Name  MA ECONOMICS 
Level of study  PG 
Semester  FIRST 
Course Name/Subject Name  Mathematical Methods for Economic Analysis 
Total Hours  90 
Course Outcomes
CO Number  Description  CO Evaluation methods 
CO1  This is a course on the basic mathematical methods necessary for understanding modern economics literature. Mathematics provides a logical, systematic framework within which quantitative relationships may be explored, and an objective picture of the reality may be generated. The deductive reasoning about social and economic phenomena naturally invites the use of mathematics. Among the social sciences, economics has been in a privileged position to respond to that invitation, since two of its central concepts, commodity, and price, are quantified in a unique manner. Thus, a good understanding of mathematics is indispensable for better cognizance of almost all fields of economics, both applied and theoretical. The goal of the course is to make students understand, assimilate and thus capable of using the mathematics required for studying economics at the master’s level. This course will focus on developing the mathematical tools that are used extensively in Microeconomics, Macroeconomics, and Econometrics. Students should be given an introduction to the Linear algebra, Differential Calculus, Integral Calculus, etc. These mathematical methods would help students in their understanding of advanced and core courses in Economics. The aim of this course is to: (i) introduce the students to several mathematical tools used in modern economics; (ii) illustrate the use of these tools by applying them to various wellknown economic models; and (iii) complement the core postgraduate microeconomic and macroeconomic theory courses. Learning outcomes: On completion of this unit, successful students should be able to demonstrate understanding of static optimization and dynamic systems applicable to economics.  Assignment, Test, Viva, Seminar 
Module 1  Hours : 15  
Syllabus: Linear algebra
Definitions of vector and matrix. Types of matrices, Addition, subtraction and multiplication of matrices. Determinants, Minors, Cofactors, Adjoint and Inverse of a matrix. Solution of a system of linear equations – Cramer’s rule and Inversion method. Rank of a matrix Linear independence of vectors. Some applications in Economics – Input output analysis – Partial equilibrium market model.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO1  Definitions of vector and matrix. Types of matrices, Addition, subtraction and multiplication of matrices. Determinants, Minors, Cofactors, Adjoint and Inverse of a matrix.  5  Lecture, PPT, Problem solving  
2  CO1  Solution of a system of linear equations – Cramer’s rule and Inversion method.  4  Lecture, PPT, Problem solving  
3  CO1  Rank of a matrix Linear independence of vectors.  4  Lecture, PPT, Problem solving  
4  CO1  Some applications in Economics – Input output analysis – Partial equilibrium market model.  2  Lecture, PPT, Problem solving  
Module 2  Hours : 25  
Syllabus:Differential Calculus
Limit of a function – Derivative of a function. Rules of differentiation – Higher order derivatives – L’Hospital rule of finding the limit of a function. Differentiation of implicit function – Partial and total derivative of a function with several variables. Maxima and minima of a function. Curvature properties – Convexity and concavity – Points of inflection. Properties of homogeneous functions – Euler’s theorem. Matrix calculus: Rules of Matrix differentiation, differentiation of a matrix by a scalar, differentiation of a scalar by a matrix. Some applications in Economics Derivation of Marginal cost, Marginal revenue functions – Derivation of point elasticity, tax yield and income multiplier, problems relating to indifference curve and isoquant. Production function, utility functions, cost functions. CobbDouglas production function, CES production function – Comparative static analysis of market model, national income model, input output model, determination of partial elasticities of demand.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO1  Limit of a function – Derivative of a function. Rules of differentiation – Higher order derivatives – L’Hospital rule of finding the limit of a function. Differentiation of implicit function – Partial and total derivative of a function with several variables. Maxima and minima of a function.  7  Lecture, PPT, Problem solving  
2  CO1  Curvature properties – Convexity and concavity – Points of inflection. Properties of homogeneous functions – Euler’s theorem.  5  Lecture, PPT, Problem solving  
3  CO1  Matrix calculus: Rules of Matrix differentiation, differentiation of a matrix by a scalar, differentiation of a scalar by a matrix.  5  Lecture, PPT, Problem solving  
4  CO1

Some applications in Economics Derivation of Marginal cost, Marginal revenue functions – Derivation of point elasticity, tax yield and income multiplier, problems relating to indifference curve and isoquant. Production function, utility functions, cost functions. CobbDouglas production function, CES production function – Comparative static analysis of market model, national income model, input output model, determination of partial elasticities of demand.  8  Lecture, PPT, Problem solving  
Module 3  Hours : 25  
Syllabus: Integral Calculus
Indefinite integrals – rules of integration, initial conditions and boundary conditions. Integration by substitution, Integration by parts – Integration of natural exponential functions. Definite integrals – properties of definite integrals. Area under a curve, area between curves. Difference equations and differential equations (basic concepts only). Improper integrals – Beta and Gamma integrals. Some applications in Economics – Consumer surplus and producer surplus – continuous interestdiscount calculation. Cobweb model, multiplier accelerator. Harrod – Domar and Solow model.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO1  Indefinite integrals – rules of integration, initial conditions and boundary conditions. Integration by substitution, Integration by parts – Integration of natural exponential functions. Definite integrals – properties of definite integrals.  9  Lecture, PPT, Problem solving  
2  CO1  Area under a curve, area between curves. Difference equations and differential equations (basic concepts only). Improper integrals – Beta and Gamma integrals.  8  Lecture, PPT, Problem solving  
3  CO1  Some applications in Economics – Consumer surplus and producer surplus – continuous interestdiscount calculation. Cobweb model, multiplier accelerator. Harrod – Domar and Solow model.  8  Lecture, PPT, Problem solving  
Module 4  Hours : 25  
Syllabus:
Linear Programming Formulation of LPP and solution using graphical and Simplex methods. Duality theory – constrained optimization with inequality and nonnegativity constrains. KuhnTucker formulation. Primal and duel, shadow prices. Applications from Economics and Finance.


Slno  CO Number  Topic /Activity  No of hours  Instructional methods to be used  
1  CO1  Formulation of LPP and solution using graphical and Simplex methods.  7  Lecture, PPT, Problem solving  
2  CO1  Duality theory – constrained optimization with inequality and nonnegativity constrains.  7  Lecture, PPT, Problem solving  
3  CO1  Duality theory – constrained optimization with inequality and nonnegativity constrains.  7  Lecture, PPT, Problem solving  
4  CO1  Applications from Economics and Finance.  4  Lecture, PPT, Problem solving  