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Paper 4 (9164, Section A) · November 2010 · Discrete random variables

A discrete random variable X has $P(X=x)=\dfrac{x-1}{16}$ for $x=2,3,4,5$ and $P(X=x)=\dfrac{9-x}{16}$ for $x=6,7,8$ . Calculate $E(X)$ .

Model answer

5

Also accepted: E(X)=5, E(X) = 5, 5,0, 5.0

Explanation

The probabilities are

\frac{1}{16},\frac{2}{16},\frac{3}{16},\frac{4}{16},\frac{3}{16},\frac{2}{16},\frac{1}{16}

for

x=2

to

x=8

, and they sum to 1. Then

E(X)=\sum xP(X=x)=\dfrac{2+6+12+20+18+14+8}{16}=\dfrac{80}{16}=5

.

Derived from ZIMSEC Statistics Paper 4, November 2010, Q1

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