Discrete random variables: probability distributions, expected value and standard deviation

Learning objectives

Construct the probability distribution of a discrete random variable as a table, a graph or a rule, from probability rules or from the results of a simulation, and check that every probability lies between 0 and 1 and that they sum to 1

Construct a cumulative probability distribution, and use it or the probability distribution itself to find the probability that the variable is at most, at least or between stated values

Calculate the mean or expected value of a discrete random variable as μ = Σ x·P(x), and interpret it in context as a long-run average rather than a value the variable must take

Calculate the variance and the standard deviation of a discrete random variable using σ = √(Σ (x − μ)²·P(x)), and interpret the standard deviation as the typical distance of the variable from its mean

Explain that the mean and the standard deviation of a random variable are parameters, fixed values describing the whole distribution, and distinguish them from statistics calculated from observed data