Suppose X1, X2, . . . are a sequence of iid uniform random variables with probability...

Suppose X1, X2, . . . are a sequence of iid uniform random variables with probability density function f(x) = 1 for 0 < x < 1, or 0, otherwise.

Let Y be a continuous random variable with probability density function g(y) = 3y² for 0 < y < 1, or 0, otherwise.

We further assume that Y and X1, X2, . . . are independent. Let T = min{n ≥ 1 : X_n < Y }. That is, T is the first time to get a smaller value than Y in the sequence {X_n} ^∞_n=1(from n=1 to infinity).

(a) Find P(T = 2) = P(X₁ ≥ Y, X₂< Y ).

(b) Find E(T).

(c) Find Var(T)

Expert Solution

orchestra answered 1 year ago

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