General discrete random variables

Mathematical Methods · Unit 3 — Further calculus and introduction to statistics · Discrete random variables

Learning objectives (6)

LO-1Determine and use the mean (expected value) of a discrete random variable as a measurement of centre, 𝐸(𝑋) = 𝜇 = ∑ 𝑝𝑖 𝑥𝑖 where 𝑝𝑖 is the probability of outcome 𝑥𝑖 occurring.LO-2Determine and use the standard deviation of a discrete random variable, √𝑉𝑎𝑟(𝑋), as a measure of spread.LO-3Determine and use the variance of a discrete random variable as a measure of spread, 𝑉𝑎𝑟 (𝑋) = ∑ 𝑝𝑖 (𝑥𝑖 − 𝜇)2 where 𝑝𝑖 is the probability of outcome 𝑥𝑖 occurring, 𝜇 is the mean.LO-4Model and solve problems that involve discrete random variables and associated probabilities, with and without technology.LO-5Understand the concepts of a discrete random variable and its associat ed probability function, and its use in modelling data.LO-6Use relative frequencies obtained from data to determine point estimates of probabilities associated with a discrete random variable.

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