Let U1,U2 be independent uniform variables on [0,1] and let T be an exponential variable with rate 1.

(a) Compute P(U1 < T,U2 < T).

(b) Compute the conditional density of T given {U1 < T , U2 < T }.

Please simplify your answers as much as possible (i.e., do not leave integrals or summations in your answer).