Concept of a random variable; Discrete and continuous random variables; Probability
function of a random variable; Distribution functions; Expectation, Variance, Moment generating functions and characteristic functions; Standard probability distributions: binomial, Bernoulli, Poisson, geometric, negative binomial, hypergeometric, uniform, exponential, normal, the Poisson and binomial approximation to the normal; Deriving distributions: the T~, ~ and F~ sampling distributions; Probability generating functions of common distribution;. The Chebyshev's inequality; the weak and strong laws of large numbers; the central limit theorem; asymptotic distributions, Limiting distributions, asymptotic estimation properties, probability limit.
function of a random variable; Distribution functions; Expectation, Variance, Moment generating functions and characteristic functions; Standard probability distributions: binomial, Bernoulli, Poisson, geometric, negative binomial, hypergeometric, uniform, exponential, normal, the Poisson and binomial approximation to the normal; Deriving distributions: the T~, ~ and F~ sampling distributions; Probability generating functions of common distribution;. The Chebyshev's inequality; the weak and strong laws of large numbers; the central limit theorem; asymptotic distributions, Limiting distributions, asymptotic estimation properties, probability limit.