The cdf of checkout duration X at a grocery store, where x is the number of minutes is F(x)= ⎩
⎨
⎧
​
0
4
x 2
​
1
​
x<0
0≤x<2
2≤x
​
Use this to compute the following: a. P(X<1) b. P(0.50.5) d. The median duration [hint: solve for 0.5=F(x ∗
) ] e. The density function f(x)=F ′
(x).