Question: A system consists of components A and B connected in parallel. Suppose the two components fail independently, and the time to failure for each component is a uniform(0, 1) random variable.
(a) Find the PDF of the time to failure of the system. (Hint. If X, Y are the times components A, B fail, respectively, the system fails at time T = max{X, Y}. Find the CDF of T from P(T ≤ t) = P(X ≤ t)P (Y ≤ t) and the CDF of a uniform(0, 1) random variable. Then find the PDF by differentiation.)
(b) Find the expected value and variance of the time to failure of the system.