Unit - 1
Introduction and Overview
The distinction between populations and samples and between population parameters and sample statistics. Pictorial Methods in Descriptive Statistics; Measures of Location and Variability.
Devore: Ch 1

Unit - 2
Elementary Probability Theory
Sample spaces and events; probability axioms and properties; counting techniques; conditional probability and Bayes’ rule; independence
Devore: Ch 2 Hogg, Tanis and Zimmerman: Ch 1

Unit - 3
Random Variables and Probability Distributions
Defining random variables; probability distributions; expected values and functions of random variables.
Devore: Ch 3 (3.1-3.3), Ch 4 (4.1-4.2) Hogg, Tanis and Zimmerman: Ch 2 (2.1-2.2), Ch 3.1

Unit - 4
Sample Distributors
Sample Distributions Properties of commonly used discrete and continuous distributions (uniform, binomial, exponential, Poisson, hypergeometric and Normal random variables). 
Devore: Ch 3 (3.4-3.6) except negative binomial distribution, Ch 4 (4.3-4.4) except gamma distribution Hogg, Tanis and Zimmerman: Ch 2 (2.4, 2.5 and 2.7), Ch 3 (3.2-3.3) except gamma and chi-square distributions (MGF treatment of distributions is not included)

Unit - 5
Random sampling and jointly distributed random variables
Density and distribution functions for jointly distributed random variables; computing expected values of jointly distributed random variables; conditional distributions and expectations, covariance and correlation.
Devore: Ch 5.1-5.3 (except pgs 200-202), 5.4, 5.5 Hogg, Tanis and Zimmerman: Ch 4 (4.1-4.4) [Double integration can be kept simple]

References Books
1. Devore, J. (2012). Probability and Statistics for Engineers, 8th ed. Cengage Learn-ing.
2. Hogg, R., Tanis, E., Zimmerman, D. (2021) Probability and Statistical inference, 10th Edition, Pearson.
3. Miller, I., Miller, M. (2017). J. Freund's Mathematical Statistics with Applications, 8th ed. Pearson.