Paper 4 · continuous random variables

The continuous random variable $X$ has probability density function $f(x)=\frac{1}{28}(6x-4)$ for $2\le x\le4$ (and 0 otherwise). Find $E(X)$ , giving your answer as a fraction or correct to 3 decimal places.

Model answer

22/7

Also accepted: 3.143, 3.14

Explanation:

E(X)=\int_2^4 x\cdot\frac{1}{28}(6x-4)\,dx=\frac{1}{28}\int_2^4(6x^2-4x)\,dx=\frac{1}{28}\left[2x^3-2x^2\right]_2^4=\frac{1}{28}(96-8)=\frac{88}{28}=\frac{22}{7}\approx3.143

Derived from ZIMSEC Statistics Paper 4, June 2009, Q2

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