36 exam-style questions on Discrete random variables; expected value — topic 4.7 of Statistics and Probability in the IB Mathematics: Applications and Interpretation syllabus — with answers and explanations. Samples below; the full set is free with an account.
A game pays $5 with probability 0.2 and $0 otherwise. Find the expected payout.
Answer: $1.00
E(X) = 5 × 0.2 + 0 × 0.8 = $1.00.
A discrete random variable X has P(X = 1) = 0.2, P(X = 2) = k, P(X = 3) = 0.3 and P(X = 4) = 0.1. Determine the value of k.
Answer: 0.4
Probabilities sum to 1: 0.2 + k + 0.3 + 0.1 = 1, so k = 0.4.
A discrete random variable X takes values 1, 2, 3 with probabilities 0.5, 0.3, 0.2 respectively. Calculate E(X).
Answer: 1.7
E(X) = 1(0.5) + 2(0.3) + 3(0.2) = 0.5 + 0.6 + 0.6 = 1.7.
A fair four-sided die shows the scores 1, 2, 3, 4. Determine the expected score of a single roll.
Answer: 2.5
E(X) = (1 + 2 + 3 + 4)/4 = 10/4 = 2.5.
A game costs $2 to play. It pays $6 with probability 0.25 and nothing otherwise. Calculate the expected net gain per game for the player.
Answer: −$0.50
Expected winnings = 6 × 0.25 = $1.50; net gain = 1.50 − 2 = −$0.50.
The probability distribution of X is given by P(X = x) = x/10 for x = 1, 2, 3, 4. Calculate E(X).
Answer: 3.0
E(X) = Σ x·P(X=x) = 1(0.1) + 2(0.2) + 3(0.3) + 4(0.4) = 0.1 + 0.4 + 0.9 + 1.6 = 3.0.
That was 6 of 36 Discrete random variables; expected value questions.
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36 Discrete random variables; expected value questions — free with an account. Spaced repetition, streaks and full exam simulations included.
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