Basic notions of probability, conditional probability and independence, Bayes’ theorem, random variables and distributions, expectation and variance, conditional expectation, moment generating functions, limit theorems. Samples and sampling distributions, estimation of parameters, testing of hypotheses, regression, correlation and analysis of variance.
Suggested books and references:
Ross, S., Introduction to Probability and Statistics for Engineers and Scientists, Academic Press; 4th ed. (2009),
Freedman, Pisani and Purves, Statistics, Viva Books; 4th ed. (2011).
Feller, W., An Introduction to Probability Theory and its Applications - Vol. 1, Wiley; 3rd ed. (2008).
Ross, S., A First Course in Probability, Pearson Education; 9th ed. (2013).
Athreya, S., Sarkar, D. and Tanner, S., Probability and Statistics (with Examples using R), Unfinished book.