Exam-Style Question on Probability Density Function

Question id: 628. This question is similar to one that appeared on an IB AA Higher paper in 2022. The use of a calculator is not allowed.

The continuous random vanable $X$ has probability density function:

$$ f(x) = \begin{cases} \dfrac{k}{\sqrt{16-x^2}}, & 0 \le x \le 2 \\ 0, & \text{ otherwise } \end{cases}$$

(a) Find the value of $k$

(b) Show that $E(X) = \dfrac{12(2-\sqrt{3})}{\pi}$

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Exam-Style Question on Probability Density Function

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