Methods2025 Exam 2 Section A · Q14CAS active1 mark

Finding k for a piecewise trigonometric pdf

Let $f$ be the probability density function for a continuous random variable $X$ , where

$f(x)=\begin{cases} k\sin(x) & 0 \le x < \dfrac{\pi}{4} \\ k\cos(x) & \dfrac{\pi}{4} \le x \le \dfrac{\pi}{2} \\ 0 & \text{otherwise} \end{cases}$

The value of $k$ is

1 mark

\frac{1}{\sqrt{2}}

\frac{1}{2-\sqrt{2}}

\sqrt{2}+2

2-\sqrt{2}

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