The cdf of checkout duration X for a book on a 2-hour reserve at a college library is given by: $$F ( x ) = \left\{ \begin{array} { l l } 0 & x

Question

The cdf of checkout duration X for a book on a 2-hour reserve at a college library is given by: $$F ( x ) = \left\{ \begin{array} { l l } 
0 & x < 0 \
\frac { x ^ { 2 } } { 4 } & 0 \leq x < 2 \
1 & 2 \leq x
\end{array} \right.$$ Use this cdf to compute the following: 
a. $P ( X \leq 1 )$ 
b. $P ( .5 \leq X \leq 1 )$ 
c. $P ( X > 5 )$ 
d. The median checkout duration $\bar { \mu } [ H \text { int: solve } .5 = F ( \bar { \mu } ) ]$ 
e. $F ^ { \prime } ( x ) \text { to obtain the density function } f ( x )$

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The Answer of The cdf of checkout duration X for a book on a 2-hour reserve at a college library is given by: $$F ( x ) = \left\{ \begin{array} { l l } 
0 & x < 0 \
\frac { x ^ { 2 } } { 4 } & 0 \leq x < 2 \
1 & 2 \leq x
\end{array} \right.$$ Use this cdf to compute the following: 
a. $P ( X \leq 1 )$ 
b. $P ( .5 \leq X \leq 1 )$ 
c. $P ( X > 5 )$ 
d. The median checkout duration $\bar { \mu } [ H \text { int: solve } .5 = F ( \bar { \mu } ) ]$ 
e. $F ^ { \prime } ( x ) \text { to obtain the density function } f ( x )$

The Cdf of Checkout Duration X for a Book on a 2-Hour