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Topic 2: Discrete Random Variables

3 dot points, in syllabus order. Each dot point has a focused answer, with exam-style questions and worked answers where available.

How do we describe the possible outcomes of a chance experiment and their probabilities?

A discrete random variable assigns a numerical value to each outcome, and its probability distribution lists every value together with its probability.

What a discrete random variable is, how to build and read a probability distribution table, and the two rules every valid distribution must satisfy.

7 min read →

How do we measure the centre and spread of a discrete probability distribution?

The expected value is the long-run mean of a discrete random variable; the variance and standard deviation measure how spread out its values are.

How to compute the expected value, variance and standard deviation of a discrete random variable, including the shortcut variance formula and linear transformation rules.

8 min read →

How do we model the number of successes in a fixed number of independent trials?

The Bernoulli distribution models a single success/failure trial, and the binomial distribution counts successes across n independent trials with constant probability.

When to use the binomial distribution, its probability formula, the mean and variance results, and how to recognise the four binomial conditions.

9 min read →