Probability Distributions Questions with Solutions

A random variable assigns a number to each outcome of a random experiment, and its probability distribution lists the probability of each value. This topic covers discrete random variables and their probability mass functions, continuous random variables and their probability density functions, and the cumulative distribution function. It also covers the expected value (mean) E(X) = sum of x p(x), the variance Var(X) = E(X^2) - [E(X)]^2, and the standard deviation. A common question type gives a probability distribution with an unknown constant k. Since all probabilities must add up to 1 (or the density must integrate to 1), you can find k first and then answer the rest of the question. Questions also ask you to build the distribution from a situation, such as the number of heads when three coins are tossed. Practise the probability distribution questions below, each with a step-by-step solution.