Further distribution concepts: Application of conditional expectation and variance, a random number of a random variable; sampling distribution of a statistic; Poisson distribution and Poisson processes; multinomial experiments. Transformation of random variables: Functions of one-dimensional random variables; the convolution theorem; distribution of a function of a random variable; Jacobian transformation; function of bivariate random variable; some applications – the Beta-distribution family; the Gamma, Chi-square, t –  and  F – distributions. Generating functions: characteristic functions; moment generating function of Beta and Gamma random variables; moment generating function of a function of a random variable; probability generating functions; some applications. Limiting Distributions: Limiting distribution function of a random variable (with proofs); the central limit theorem; law of large numbers; some applications – limiting form of the Binomial distribution; approximation to the Poisson distribution. Concepts of convergence: convergence in probability; convergence in mean square; Chebyshev inequality.