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LearnCambridge97092026–2027Paper 5 · Probability & Statistics 1Discrete random variables

Paper 5 · Module

Discrete random variables

4 subtopics≈ 130 min in total

Start the module: Probability distributions Open graphing calculator

Probability distributions
A random variable turns the outcome of an experiment into a number. Listing each possible value with its probability gives a distribution table, and the probabilities must add up to $1$ .
≈ 30 min
Expectation and variance
The expectation $E(X)$ is the long-run average value of $X$ : each value weighted by its probability. The variance measures the spread, using the same "mean of the squares minus the square of the mean" idea as for data.
≈ 30 min
The binomial distribution
Count the successes in $n$ independent trials, each with the same chance $p$ . The probability of exactly $r$ successes is $\binom nr p^r(1-p)^{n-r}$ : choose which trials succeed, then multiply.
≈ 40 min
The geometric distribution
How long until the first success? If each trial succeeds with probability $p$ , the first success comes on trial $r$ with probability $(1-p)^{r-1}p$ : $r-1$ failures, then a success.
≈ 30 min