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LearnAQA7367First teaching 2017Paper 3 · Statistics optionDiscrete random variables
Paper 3 · Module

Discrete random variables

3 subtopics≈ 95 min in total
Start the module: Probability distributionsOpen graphing calculator

  1. 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 11.

    ≈ 30 min

  2. Expectation and variance

    The expectation E(X)E(X) is the long-run average value of XX: 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

  3. Expectation, variance and the discrete uniform distribution

    E(X)=∑xP(X=x)E(X)=\sum xP(X=x) is the long-run average. Var(X)=E(X2)−[E(X)]2\text{Var}(X)=E(X^2)-[E(X)]^2 measures spread. For linear changes, E(aX+b)=aE(X)+bE(aX+b)=aE(X)+b but Var(aX+b)=a2Var(X)\text{Var}(aX+b)=a^2\text{Var}(X): adding a constant shifts values without spreading them.

    ≈ 35 min