III. USING CONDITIONALS Let X > 0 be a positive random variable. Define Y in terms...

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III. USING CONDITIONALS Let X > 0 be a positive random variable. Define Y in terms of X as follows: Given that x = x, Y is Poisson with A= x. That is, P[Y = k|X = x] = e-® for all k E {0,1,2, ...}. a) Compute E [Y|X = 1/4] and E[Y] assuming that X - b) Compute E [Y|X = 1/4] and E[Y] assuming that X ~ Uniform[10, 20]. c) Compute E[Y|X = 1/4] and E [Y] assuming that X ~ Geom(p). d) Compute E [Y]X = 1/4] and E [Y] assuming P[X = 1] = P[X = 2] = 1/2. Exp(A). III. USING CONDITIONALS Let X > 0 be a positive random variable. Define Y in terms of X as follows: Given that x = x, Y is Poisson with A= x. That is, P[Y = k|X = x] = e-® for all k E {0,1,2, ...}. a) Compute E [Y|X = 1/4] and E[Y] assuming that X - b) Compute E [Y|X = 1/4] and E[Y] assuming that X ~ Uniform[10, 20]. c) Compute E[Y|X = 1/4] and E [Y] assuming that X ~ Geom(p). d) Compute E [Y]X = 1/4] and E [Y] assuming P[X = 1] = P[X = 2] = 1/2. Exp(A).