(a)[3]
Hence, show that $a = \dfrac{27}{2}$.
(b)[3]
Hence, show that $\text{E}(X) = \dfrac{27}{2} \ln \dfrac{3}{2} - 3$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The probability density function $f$ for a random variable $X$ is specified by $$f(x) = \begin{cases} \dfrac{a}{x^2} - \dfrac{18}{x^3}, & 2 \le x \le 3, \\ 0, & \text{otherwise}, \end{cases}$$ where $a$ is a constant.
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This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Make an attempt to integrate $f(x)$: $\int_2^3\left(\dfrac{a}{x^2}-\dfrac{18}{x^3}\right)dx=1$” …
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