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LearnEdexcelYMA012018 specificationWST01 · Statistics 1Discrete random variables
WST01 · Module

Discrete random variables

2 subtopics≈ 65 min in total
Start the module: Probability distributions and the CDFOpen graphing calculator

  1. Probability distributions and the CDF

    A discrete random variable takes separate values, each with a probability. All the probabilities add to 11, which lets you find unknown constants. The cumulative distribution function F(x)=P(X≤x)F(x)=P(X\le x) is a running total; subtract consecutive values to get back P(X=x)P(X=x).

    ≈ 30 min

  2. 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