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
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To find the median of a continuous variable you solve:
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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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For a continuous random variable, P(X = 3) equals:
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Which statement about E(X) for a discrete random variable is correct?
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If f(x) = kx on [0, 4], the equation that gives k is:
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If all probabilities in a table sum to 0.9, then:
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The mode of a continuous random variable is:
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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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X has pdf f(x) = (3/8)x² for 0 ≤ x ≤ 2 and 0 elsewhere. Find P(X < 1).
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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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If a pdf is symmetric about x = 5, its mean is:
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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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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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X has P(X=−1)=0.25, P(X=0)=0.5, P(X=1)=0.25. Find Var(X).
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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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f(x) = (3/8)x² on [0, 2]. P(X < 2) equals:
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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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