Syllabus (ECONOMICS)

Course Type: MAJ-10

Semester: 6

Course Code: BECOMAJ10T

Course Title: Statistics - II

(L-P-Tu): 5-0-1

Credit: 6

Practical/Theory: Theory

Course Objective:

Learning Outcome: Course Objective After completion of this course involving probability and statistical inference, the learner will be able to formulate relevant numeric problems from real life situations and use appropriate techniques to solve them. The learner will also

Unit 1: Probability: (15)

1. Why study this unit, real life problems which can be answered after studying this unit; Random Experiment, Trial, Outcome, Event, Mutually Exclusive Events, Exhaustive Events, Equally Likely Events, Complementary Events (1)
2. Classical Definition of Probability and its limitations, Applications (2)

(c ) Axiomatic Approach to Probability – Rationale, Sample space and events, Additive Theorem of Probability for two and three events, Applications (2)

(d ) Conditional Probability, Independence of Events – Definition, Concept, Applications (2)

(e) Bayes’ Theorem – Statement, Proof, Applications (2)

(f) Probability Distribution – Random/Stochastic Variable, Expectation, Variance, Applications (3)

(g) Joint Probability Distribution (only for discrete variable) – Concept, Applications (3)

Note: Calculations of permutation and combinations are not to be shown in answers, they can be found using calculators

Unit 2: Theoretical Distributions: (18)

1. Why study this unit, real life problems which can be answered after studying this unit; Probability Function – pmf and pdf, their properties, Applications (2)
2. Distribution Function – Definition, Derivation of distribution function from probability function and vice versa (for both discrete and continuous variables) (2)

(c ) Binomial Distribution – Uses, Properties (derivation of mean, variance and mode only), Applications (2)

(d ) Poisson Distribution – Uses, Properties (derivation of mean, variance and mode only), Applications, Poisson Distribution as a limiting case of Binomial Distribution (2)

(e) Normal Distribution – Uses, Properties (proofs not required), Standard Normal Variable & its properties (proofs not required), Applications (3)

(f) Fitting of Binomial, Poisson, and Normal Distributions to observed distributions (goodness of fit is not to be checked here) (3)

(g) Hypergeometric, Uniform and Rectangular Distributions – Concept only (no properties, no applications) (1)

(h) Factorial Moments and Moment Generating Functions – Purpose, Definition, derivation and application of Moment Generating Functions for Binomial and Poisson Distributions (3)

Note: While answering, values of e^a are to be found using calculators; calculations of permutation and combinations are not to be shown in answers, they can be found using calculators

Unit 3: Sampling Theory: (6)

1. Why study this unit, real life problems which can be answered after studying this unit; Difference between Population and Sample, Advantages and Disadvantages of sample survey over population survey, Principal steps in a sample survey (1)
2. Random and non-random sampling techniques, SRSWR and SRSWOR – Properties, Method of drawing samples using Random Numbers, introduction to Random Number Tables (2)

(c ) Difference between Parameter and Statistic, Sampling Distribution, Numeric problems on calculation of Expectation and Standard Error from Sampling Distribution, Derivation of Expectation and Standard Error of Sample Mean and Sample Proportion under SRSWR and SRSWOR (3)

Unit 4: Statistical Inference: (32)

1. Why study this unit, real life problems which can be answered after studying this unit; Purpose of Inferential Statistics, concept and difference between estimation and testing of hypothesis, difference between test of hypothesis and test of significance (1)
2. Difference between point estimation and interval estimation, difference between OLS estimation, MLM, and Method of Moments (1)

(c ) Properties of a good estimator, MVUE, BLUE, Applications (only numeric problems, no theoretical proofs) (3)

(d ) Maximum-Likelihood-Estimation – Definition, Properties (no application), Method of Moments – only concept (1)

(e) Null and Alternative Hypothesis, One-tailed and Two-tailed Tests, Type I and Type II Errors, power of a test, confidence interval, level of significance, critical region, region of acceptance, p-value, steps in testing of hypothesis (4)

(f) Concept of Degrees of Freedom (1)

(g) z, t, χ², and F Distributions – Definition and Properties (no proof), how to find values from distribution tables (2)

(h) Scope of application of z, t, χ², and F statistic in hypothesis testing – which one is to be used in what situation (2)

(i) Numeric problems only on application of z and t statistic in hypothesis testing, derivation of confidence interval for population mean and proportion and their application, use of t in checking goodness of fit of normal distribution to observed distribution (8)

(j) Application of χ² statistic and Fisher’s Exact Test for testing independence of two attributes, and in checking goodness of fit of Binomial and Poisson Distributions to observed distribution (2)

(k) ANOVA (only one-way) – Purpose, Steps, Applications (6)

(l) ANOVA (two-way) – only introductory concept (no detailed discussion, nor applications) (1)

Unit 5: Vital Statistics: (4)

1. Why study this unit, real life problems which can be answered after studying this unit; Different measures of Birth, Death, and Fertility rates (2)
2. Life Table – Uses, construction, and simple applications (2)

Reading References:

1. Goon, A. M., Gupta, M. K., & Dasgupta, B.,2013, Fundamentals of Statistics (Volume I and II), The World Press Private Ltd.
2. Mood, A.M, Graybill, F. A, & Boes, D.C., 1974, Introduction to The Theory of Statistics, McGraw Hill.
3. John E. Freund, 1992, Mathematical Statistics, Prentice Hall.
4. R. Ganesan and PV Sreenivasaiah, 2015, Textbook of Statistics, Write and Print Publication, 1^st edition.
5. SS Gupta and VK Kapoor, 2020, Fundamentals of Mathematical Statistics, 12^th edition, Sultan Chand & Sons.
6. NG Das, 2017, Statistical Methods (Combined Volume), McGraw Hill Education, Kolkata.
7. R.V. Hogg and A.T. Craig, An Introduction to Mathematical Statistics, Third Edition, Amerind, New York, London.
8. Shantilal R. Patel, 2021, Statistical Inference, IK International Pvt. Ltd.
9. Robert V. Hogg, Elliot Tanis and Dale Zimmerman, 2020, Probability and Statistical Inference, Pearson India.