Probability & Statistics 2 — Variant 2

A Level Mathematics · 9709/62 · May/June 2020

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Questions

1 of 6 questions shown here, checked against the paper. The others are in the PDF above — they contain diagrams or maths we could not yet verify, and we would rather show you the original than a transcription we are not sure of.

6
A random variable XX has probability density function given by f(x)={kx21⩽x⩽a,0otherwise,\mathrm{f}(x) = \begin{cases} \frac{k}{x^{2}} & 1 \leqslant x \leqslant a, \\ 0 & \text{otherwise}, \end{cases} where kk and aa are positive constants.
6(a) [3]
Show that k=aa−1k = \frac{a}{a - 1}.
6(b) [3]
Find E(X)\mathrm{E}(X) in terms of aa.
6(c) [4]
Find the 60th percentile of XX in terms of aa.

Published by Cambridge Assessment International Education. Reproduced for study use.