Question: Let X Unif(0, 1). If X = x, then Y Unif(x). (a) Find P(Y < 1/4) by conditioning on X. (b) Find P(Y

Let X ∼ Unif(0, 1). If X = x, then Y ∼ Unif(x).
(a) Find P(Y < 1/4) by conditioning on X.
(b) Find P(Y < 1/4) by using the marginal density of Y .
(c) Approximate P(Y < 1/4) by simulation.

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