2. Suppose that X is a standard uniform random variable and Y|X = x ~Normal(x,x) for 0 ≤ x ≤ 1. Find V[Y].

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2. Suppose that X is a standard uniform random variable and Y|X = x ~Normal(x,x) for
0 ≤ x ≤ 1. Find V[Y].
3. Let Y be a random variable with moment generating function my (t) and X be a random
variable with mx(t) = (2e³t + 1)my(t)/3. Given that E[Y] = 10 and V[Y] = 12, find
E[X] and V[X].
Transcribed Image Text:2. Suppose that X is a standard uniform random variable and Y|X = x ~Normal(x,x) for 0 ≤ x ≤ 1. Find V[Y]. 3. Let Y be a random variable with moment generating function my (t) and X be a random variable with mx(t) = (2e³t + 1)my(t)/3. Given that E[Y] = 10 and V[Y] = 12, find E[X] and V[X].
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