Course Contents

Concept of random variable, discrete and continuous random variables, discrete probability distribution, probability function, distribution function and joint distribution, continuous probability distribution, probability density function and distribution function, Independence of two random variables. Mathematical Expectation, expectation of a function of random variable and its properties, mean, variance and moments of simple discrete and continuous probability distributions. Definition of moment generating function with its properties and covariance. Binomial, Hypergeometric, Poisson distribution (applications only), their fittings to statistical data and also moment generating functions. Negative Binomial distribution, Geometric distribution and Multinomial distribution (Application only). Normal and Exponential distributions with mean, variance and moment generating functions, also fitting to statistical data. Normal approximation to Binomial and Poisson distribution (application only). Case Study: Analysis of real data based on the above contents, presented in the form of a report.

Course Synopsis

Introduction to the concept of random variable and probability distribution. Application of some important discrete and continuous probability distributions.

Course Learning Outcomes

On completion of the course students should be able to differentiate between discrete and continuous random variables and also find the mean & spread out of it. They also will solve the problems relating different probability distributions.