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Find the value of $\text{E}(X)$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The random variable $X$ is given the probability density function $f$, with $f(x) = \begin{cases} \frac{3}{2}(1 - x^2), & 0 \leq x \leq 1, \\ 0, & \text{otherwise}. \end{cases}$
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This 3-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Try to integrate $x f(x)$, namely $\frac{3}{2}\int_0^1 (x - x^3)\,dx$, while omitting the limits” …
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