Q48

Consider a probability distribution given by the density function $P(x)$.

$$P(x)=\left\{\begin{aligned} C x^{2}, & \text { for } 1 \leq x \leq 4 \\ 0, & \text { for } x\lt1 \text { or } x>4 \end{aligned}\right.$$

The probability that $x$ lies between $2$ and $3$, i.e., $P(2 \leq x \leq 3)$ is _________. (rounded off to three decimal places)