Chapter 12, Problem 12RE

(a)

To determine

To calculate: The density function for $X$, where the random variable $X$ has a cumulative distribution function $F\left(x\right)=\left(x^2-9\right)/16$ on $3\le x\le 5$.

(b)

To determine

To calculate: $a$ such that $\mathrm{Pr}\left(a\le X\right)=\frac{1}{4}$, where the random variable $X$ has a cumulative distribution function $F\left(x\right)=\left(x^2-9\right)/16$ on $3\le x\le 5$.