# Probability, Statistics and Stochastic Processes, Jul-Nov 2021

### Instructor

Sivaram Ambikasaran,

### Syllabus

**Probability**
Axiomatic definition of probability, Independent Events, Baye's theorem, Discrete and continuous random variables, Distribution, Functions of random variables, Expectation, Variance, Correlation coefficient, Chebyshevâ€™s inequality, Markov inequality, Conditional expectations, Standard discrete and continuous distributions (Binomial, Poisson, Geometric, Exponential, Normal, Chi-square), Moment generating function, Sums of random variables, Law of large numbers, Central limit theorem, Normal approximation to Binomial.

**Statistics**
Sampling distribution, Estimation of parameters, Maximum likelihood estimates, Confidence intervals, Studentâ€™s t-distribution, Testing hypothesis, Goodness of fit.

**Stochastic Processes**
Discrete random process, Stationary random process, Bernoulli process, Poisson process, Markov chain.

### Textbooks

*Introduction to Probability*, by Dimitri Bertsekas and John N. Tsitsiklis (referred as BT in online lectures)

### Other Reference Textbooks

*Introductory Probability and Statistical Applications*, by Paul L. Meyer (referred as PLM in online lectures)
*John E. Freund's Mathematical Statistics with Applications*, by Irwin Miller and Marylees Miller (referred as M\(^2\) in online lectures)
*Fundamentals of Applied Probability and Random Processes*, by Oliver C. Ibe (referred as Ibe in online lectures)

Click here for accessing the course materials

### More details will be added later.