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

Question

Examlex · Accepted Answer

The Answer is a.

P ( X \leq 1 ) = F ( 1 ) = \frac { 1 } { 4 } = 25

b.

P ( .5 \leq X \leq 1 ) = F ( 1 ) - F ( .5 ) = \frac { 3 } { 16 } = .1875

c.

P ( X > .5 ) = 1 - P ( X \leq .5 ) = 1 - F ( .5 ) = \frac { 15 } { 16 } = .9375

d.

.5 = F ( ilde { \mu } ) = \frac { ilde { \mu } ^ { 2 } } { 4 } \Rightarrow ilde { \mu } ^ { 2 } = 2 \Rightarrow ilde { \mu } = \sqrt { 2 } \approx 1.414

e.

f ( x ) = F ^ { \prime } ( x ) = \frac { x } { 2 } ext { for } 0 \leq x < 2 , ext { and } = 0 ext { otherwise }

Definitions: