Unit 4: Statistics and Probability

Topic 4.14: Continuous random variables (HL only) Questions

Practice 20 exam-style questions for IB Math AA SL Topic 4.14. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.

11 mark
2026
To find the median of a continuous variable you solve:
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2Find2 marks
2026
A spinner pays out X = 1, 2 or 5 dollars with P(X=1)=0.6, P(X=2)=0.3, P(X=5)=0.1. Find the expected payout E(X).
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31 mark
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For a continuous random variable, P(X = 3) equals:
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41 mark
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Which statement about E(X) for a discrete random variable is correct?
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51 mark
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If f(x) = kx on [0, 4], the equation that gives k is:
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61 mark
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For any random variable, Var(X) equals:
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7Write down1 mark
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Write down .
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81 mark
2026
A pdf must satisfy:
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91 mark
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If all probabilities in a table sum to 0.9, then:
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101 mark
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The mode of a continuous random variable is:
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11Find3 marks
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A discrete random variable X has P(X=1)=0.1, P(X=2)=0.4, P(X=3)=0.3, P(X=4)=c. Find c and E(X).
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12Find2 marks
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X has pdf f(x) = (3/8)x² for 0 ≤ x ≤ 2 and 0 elsewhere. Find P(X < 1).
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13Find2 marks
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X has pdf f(x) = (1/2)x for 0 ≤ x ≤ 2 and 0 elsewhere. Find P(1 < X < 2).
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141 mark
2026
If a pdf is symmetric about x = 5, its mean is:
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15Find3 marks
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A continuous variable T (minutes) has pdf f(t) = (3/4)t(2 − t) for 0 ≤ t ≤ 2 and 0 elsewhere. Find the mode of T.
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16Find3 marks
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X has P(X=0)=0.3, P(X=1)=0.5, P(X=2)=0.2. Find E(X) and Var(X).
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17Find3 marks
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X has P(X=−1)=0.25, P(X=0)=0.5, P(X=1)=0.25. Find Var(X).
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18Find3 marks
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X has P(X=2)=k, P(X=3)=2k, P(X=4)=2k. Find k, then E(X).
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191 mark
2026
f(x) = (3/8)x² on [0, 2]. P(X < 2) equals:
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20Find3 marks
2026
A continuous random variable X has pdf f(x) = kx for 0 ≤ x ≤ 3 and 0 elsewhere. Find the value of k.
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