Possible values of X, the number of components in a system submitted for repair that must be replaced are 1,2,3, and 4 with corresponding probabilities 0.15, 0.35, 0.35, and 0.15 respectively.
a. Calculate E(X) and then E(5-X)
b. Would the repair facility be better off charging a flat fee of $75 or else the amount $[150/(5-X]?

Given that the possible values of X, the number of components in a system submitted for repair that must be replaced are 1,2,3, and 4 with corresponding probabilities 0.15, 0.35, 0.35, and 0.15 respectively.

X 1 2 3 4

p 0.15 0.35 0.35 0.15 1

x*p 0.15 0.70 1.05 0.60 2.50

a)E(x) = 2.50

By linearity property

E(5-x) = 5-E(x) = 2.50

b) If fees it 75 then charges would be[tex]75(2.5) = 187.50[/tex]

Else repair charges = [tex]\frac{150}{E(5-x)} \\=60[/tex]

II one is better