Topic 3: Continuous random variables and the normal distribution — Maths Interactives

General continuous random variables

6 hours

Use relative frequencies and histograms obtained from data to estimate probabilities associated with a continuous random variable.
Understand the concepts of a probability density function, cumulative distribution function, and probabilities associated with a continuous random variable given by integrals; examine simple types of continuous random variables and use them in appropriate contexts. 1 interactive
Calculate the expected value, 𝐸 (𝑋) = 𝜇 = ∫ 𝑥𝑝(𝑥)𝑑𝑥 ∞ −∞, of a continuous random variable where 𝑝(𝑥) is the probability density function. 1 interactive
Calculate the variance, 𝑉𝑎𝑟(𝑋) = 𝜎 2 = ∫ (𝑥 − 𝜇)∞ −∞ 2 𝑝(𝑥)𝑑𝑥, and standard deviation 𝜎, of a continuous random variable.
Understand standardised normal variables (𝑧-values, 𝑧-scores) and use these to compare samples. 1 interactive

Normal distributions

6 hours