Question: 7. The CDF function of the checkout duration, X, in a certain supermarket, measured in minutes, is F(x) = 0 for x 0, F(x)

7. The CDF function of the checkout duration, X, in a certain supermarket, measured in minutes, is F(x) = 0 for x ≤ 0, F(x) = 1 for x > 2, and F(x) =

x2 4

for x between 0 and 2 .

(a) Find the median and the interquartile range of the checkout duration.

(b) Find E(X) and σX. You may use R commands for the needed integrations.

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