#### Statistics and Probability IMCA (Exam Sept / Oct 2021)

MI 104: Statistics and Probability Syllabus

(1) Introduction to Probability, Sample space, events, probability of an event, additive rules, conditional probability, multiplicative rule, Bayes’ rule

(2) Concept of a random variable, discrete probability distribution, continuous probability distribution, joint probability distribution, independent random variables, Chebyshev’s theorem.

(3) Mean of a random variable, variance and covariance, means and covariances of linear combinations of random variables.

(4) Some discrete probability distributions: discrete uniform distribution, binomial and multinomial distributions, hypergeometric distribution, negative binomial and geometric distribution, Poisson distribution and Poisson process.

(5) Some continuous probability distributions: continuous uniform distribution, normal distribution, area under the normal curve, applications of the normal distribution, normal ap-proximation to the binomial distribution, gamma and exponential distribution, chi-squared distribution, lognormal distribution.

(6) Functions of random variables, transformations of variables, moments and moment generating functions

(7) Statistical hypothesis: general concepts, testing a statistical hypothesis, use of p values for decision making, tests concerning a singular mean (variance known), confidence interval estimation, tests on a single mean (variance unknown).

Reference Books:

R. Walpole, R.H. Myers, S.L. Myers, and K. Ye, Probability and Statistics for Engineer sand Scientists, (Seventh Edition, Pearson India), 2011.

S Ross, A first course in probability, (Pearson, ninth edition), 2016