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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).
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).
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