2 interactive labs · AS & A Level Mathematics 9709
Probability Distribution Table, E(X) and Var(X)
5.4 Discrete random variables · Drag the bars of a distribution table, find an unknown k from Σp = 1, reject invalid values, then calculate E(X) and Var(X).
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About this lab
Drag the bars of a distribution table, find an unknown k from Σp = 1, reject invalid values, then calculate E(X) and Var(X).
You will be able to
Determine an unknown probability k from Σp = 1, and reject values that break 0 ≤ p ≤ 1.
Calculate E(X) = Σxp and E(X²) = Σx²p from a probability distribution table, exactly where the probabilities are fractions.
Calculate Var(X) = E(X²) − [E(X)]² and explain why it cannot be negative and why E(X²) is not [E(X)]².
Which Model? Binomial, Geometric or Neither
5.4 Discrete random variables · Read ten scenarios and predict B(n, p), Geo(p) or neither from the conditions, then probe the bars, P(X = r) and the mean.
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About this lab
Read ten scenarios and predict B(n, p), Geo(p) or neither from the conditions, then probe the bars, P(X = r) and the mean.
You will be able to
State the conditions for a binomial model (a fixed number of independent trials, two outcomes, constant probability of success) and for a geometric model (independent trials repeated until the first success).
Decide from a described situation whether X ~ B(n, p), X ~ Geo(p) or neither, and justify the choice by the condition that holds or fails.
Calculate P(X = r) from the formulae for B(n, p) and Geo(p), and E(X) = np, Var(X) = np(1 − p) and E(X) = 1/p.
Predict how the probabilities and the mean change when n or p changes.
