General continuous random variables

Mathematical Methods · Unit 4 — Further calculus, trigonometry and statistics · Continuous random variables and the normal distribution

Learning objectives (5)

LO-1Calculate the expected value, 𝐸 (𝑋) = 𝜇 = ∫ 𝑥𝑝(𝑥) 𝑑𝑥 ∞ −∞, of a continuous random variable where 𝑝(𝑥) is the probability density function.LO-2Calculate the variance, 𝑉𝑎𝑟 (𝑋) = 𝜎 2 = ∫ (𝑥 − 𝜇) ∞ −∞ 2 𝑝(𝑥)𝑑𝑥, and standard deviation 𝜎, of a continuous random variable.LO-3Understand standardised normal variables (𝑧-values, 𝑧-scores) and use these to compare samples.LO-4Understand 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.LO-5Use relative frequencies and histograms obtained from data to estimate probabilities associated with a continuous random variable.

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