Unit 4: Statistics and Probability
Topic 4.14: E(X), Var(X) & estimators (HL only) Questions
Practice 20 exam-style questions for IB Math AI SL Topic 4.14. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
2Find2 marks
2026
X and Y are independent with E(X) = 10, E(Y) = 4, Var(X) = 9, Var(Y) = 7. Find E(X + Y) and Var(X + Y).
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2026
The sample mean x̄ is used to estimate the population mean μ. The sample mean is:
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2026
X and Y are independent. Which statement is always TRUE?
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2026
A factory's daily output X (in tonnes) has mean 50 and standard deviation 6. Profit in pounds is W = 40X − 300 (fixed costs). State the mean and standard deviation of W.
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2026
Var(X) = 16. The variance of (−2X + 7) is:
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2026
The score X on a spinner has E(X) = 3.4 and Var(X) = 2.04. A prize of P = 10X − 5 pounds is paid. Find E(P) and the standard deviation of P.
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2026
X takes values 1 and 3 with P(X = 1) = 0.25 and P(X = 3) = 0.75. Then E(X) =
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2026
A board game costs £3 to play. Winnings W (in £) have E(W) = 2.5 and SD 1.8. Net gain is G = W − 3. Find E(G) and comment on whether a player gains on average.
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2026
An orange has mass mean 130 g, SD 12 g; a lemon has mass mean 60 g, SD 5 g; all fruit independent. Find the mean and standard deviation of (one orange − one lemon).
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2026
One ball-bearing has variance 0.04. The total of 9 independent bearings has variance:
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2026
Two independent machine parts have lengths with means 30 mm and 45 mm and standard deviations 0.5 mm and 1.2 mm. They are joined end to end. Find the mean and standard deviation of the joined length.
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2026
Independent X, Y have SD(X) = 3 and SD(Y) = 4. Then SD(X + Y) =
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2026
A discrete RV X has P(X = 0) = 0.2, P(X = 1) = 0.5, P(X = 2) = 0.3. Find E(X) and Var(X).
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2026
X has the distribution P(X = 1) = 0.1, P(X = 2) = 0.3, P(X = 3) = 0.4, P(X = 5) = 0.2. Find the standard deviation of X.
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2026
A GDC reports σx = 2.0 and Sx = 2.236 for a data set. The unbiased estimate of the population variance is:
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2026
Chocolate bars have mass with mean 45 g and SD 2 g, independently. A multipack contains 8 bars. Find the mean and standard deviation of the total mass of the multipack.
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