03:49
Probability with Applications in Engineering, Science, and Technology
Let $X$ denote the amount of time a book on 2 -h reserve is actually checked out, and suppose the cdf is
$$F(x)=\left\{\begin{array}{ll}{0} & {x<0} \\ {\frac{x^{2}}{4}} & {0 \leq x<2} \\ {1} & {2 \leq x}\end{array}\right.$$
Use this to compute the following:
(a) $P(X \leq 1)$
(b) $P(.5 \leq X \leq 1)$
(c) $P(X>1.5)$
(d) The median checkout duration $\eta[$Hint: Solve $F(\eta)=.5 .]$
(e) $F^{\prime}(x)$ to obtain the density function $f(x)$