Q1Single correct3 Marks10 May 2026

The probability density function of a random variable $X$ is given as: $$f_X(x) = \begin{cases} 0.2, & 0 \le x < 1, \\ cx, & 1 \le x < 2, \\ 0.4, & 2 \le x < 3, \\ 0, & \text{otherwise.} \end{cases}$$ Find the value of $c$.

A

$\frac{3}{15}$

B

$\frac{1}{10}$

C

$\frac{3}{10}$

D

$\frac{4}{15}$