Syllabus (STATISTICS)

Course Type: ME-5

Semester: 5

Course Code: BSTAMEA35T

Course Title: Title: Probability and Probability Distributions -II

(L-P-Tu): 3-0-1

Credit: 4

Practical/Theory: Theory

Course Objective:

Learning Outcome: This will provide the skillful development for the students regarding use of analytics

Unit 1

Continuous random variables, p.d.f. and c.d.f., illustrations and properties, univariate transformations with illustrations. Two dimensional random variables: continuous type, joint, marginal and conditional, p.d.f., and c.d.f.. Independence of two variables.

Unit 2

Mathematical Expectation (discrete and continuous): Single & bivariate random variables and their properties. Probability generating function. Moments. Moment generating function. Correlation coefficient, Conditional expectation and variance.

Probability Inequalities: Markov & Chebyshev.

Unit 3

Standard continuous probability distributions: uniform, normal, exponential, Cauchy, beta, gamma, lognormal, logistic, double exponential and Pareto along with their properties and limiting/approximation cases.

Unit 4

Bivariate Normal Distribution (BVN): p.d.f. of BVN, properties of BVN, marginal and conditional p.d.f. of BVN.

Reading References:

Hogg, R.V., Tanis, E.A. and Rao J.M. (2009): Probability and Statistical Inference, Seventh Ed, Pearson Education, New Delhi.

Miller, Irwin and Miller, Marylees (2006): John E. Freund’s Mathematical Statistics with Applications, (7th Edn.), Pearson Education, Asia.

Myer, P.L. (1970): Introductory Probability and Statistical Applications, Oxford & IBH Publishing, New Delhi.

Rohatgi, V. K. and Saleh, A.K. Md. E. (2009): An Introduction to Probability and Statistics. 2nd Edn. (Reprint) John Wiley and Sons.

Ross, S. (2002): A First Course in Probability, Prentice Hall.

Feller, W. (1968): An Introduction to Probability Theory & its Applications, Vol-I, John Wiley.