Discrete random variables

Discrete Random Variables: Distributions, Expectation and VarianceSign up

understand the concept of a discrete random variable, its probability distribution and the requirement that probabilities sum to 1 · be able to calculate the expectation E(X), variance Var(X) and standard deviation of a discrete random variable, including E(aX + b) and Var(aX + b)

The Binomial DistributionSign up

understand the conditions under which a random variable can be modelled by B(n, p): a fixed number of independent trials with two outcomes and constant probability of success · be able to calculate probabilities, expectation E(X) = np and variance Var(X) = np(1 - p) for a binomially distributed variable

The Geometric DistributionSign up

use the formula for geometric probabilities Geo(p): P(X=r)=p(1-p)^(r-1), r=1,2,3,... · recognise situations modelled by the geometric distribution (trials up to and including the first success, constant p) · use the expectation E(X)=1/p (proof not required)