Question: Let X have an exponential distribution conditioned to be greater than 1. That is, for t > 1, P(X t) = P(Y t|Y

Let X have an exponential distribution conditioned to be greater than 1. That is, for t > 1, P(X ≤ t) = P(Y ≤ t|Y > 1), where Y ∼ Exp(λ).
(a) Find the density of X.
(b) Find E[X].

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