Question

The age of cars in a parking lot goes from 6 months to 9 years. Assume that X is the distribution of the age f a car, and it is uniform.

a) What is P(X > 4)

b) Compute f(7) and F(7)

Answer 1

a)

X ~ Uniform(a = 0.5 years, b = 9 years)

P(X > x) = (b - x) / (b - a)

P(X > 4) = (9 - 4) / (9 - 0.5) = 0.5882353

b)

f(X) = 1/(b-a) = 1/(9 - 0.5) = 1/8.5 for 0.5 X 9

F(X) = (X - a) / (b-a) = (X - 0.5) / (9-0.5) = (X - 0.5) / 8.5 for 0.5 X 9

f(7) = 1/8.5 = 0.1176471

F(7) = (7 - 0.5) / 8.5 = 0.7647059