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Question: assumptions from problem 2...

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Problem 3: 10 points Continue with the same assumptions as in Problem 2. Recall that a random variable, Z, has the Gamma distribution with the density: fz (z) = λ2 z exp[-λ z] for z > 0, and fz(z) = 0, elsewhere. Conditionally given Z = z, a random variable, U, is uniformly distributed over the interval, (0, z) 1. Find conditional expectation. EZIU = ul. 2. Find conditional variance, VARZİU-ul 3. Find conditional expectation, E U Z-z] 4. Find conditional variance. VARU -2]

Assumptions from problem #2

Problem 2: 10 points A random variable, Z, has the Gamma distribution with the density: fz (z) λ2 z exp [-A z] for z > 0, and f ()0, elsewhere. According to the notation in Probability Theory, Z has the distribution Conditionally, given Z = z, a random variable, U, is uniformly distributed over the interval, (0,2). Gamma [2, λ-1]

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