Let X have a uniform distribution on the interval (2, 10).

Question

Find the probability that the sum of 2 independent observations of X is greater than 18.

Answer 1

Melissa, I have already answered nearly the exactly same problem for you.

10 - 2 = 8

f(x,y) = 1/8 * 1/8 = 1/64 on [2, 10] x [2, 10]

P(X + Y) >= 18, as 10 + 10 = 20, is 1/2 * 2^2 * 1/64 = 1/32

See other problem for details.