Textbook Problem

Finding a Probability In Exercises 19-26, sketch the graph of the probability density function over the indicated interval and find each probability. See Example 3.

$f(x)=\frac{3}{16}\sqrt{x},\left[0,4\right]$

(a) $P\left(0<x<2\right)$

(b) $P\left(2<x<4\right)$

(c) $P\left(1<x<3\right)$

(d) $P\left(x\le 3\right)$