Let X Denote the Amount of Time for Which a Book

Essay

Let X denote the amount of time for which a book on 2-hour reserve at a college-library is checked out by a randomly selected student and suppose that X $f ( x ) = \left\{ \begin{array} { l l } .5 x & 0 \leq x \leq 2 \\0 & \text { otherwise }\end{array} \right.$ Calculate the following probabilities:
a. $$P (\bar{ X} \leq 1 )$$
b. $P ( .5 \leq \bar{X} \leq 1.5 )$