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Problem 2: 15 points [= 5 + 5 + 5] Assume that a random variable (Y) follows the exponential distribution with density fY (y) = 2e-2y for y >0 and fY (y) = 0 elsewhere. Given Y = y, a random variable N is Poisson distributed with rate = y. 1. Determine marginal distribution of N. 2. Evaluate expectation of N. 3. Derive variance of N.
Problem 2: 15 points [= 5 + 5 + 5] Assume that a random variable (Y) follows the exponential distribution with density fY (y) = 2e-2y for y >0 and fY (y) = 0 elsewhere. Given Y = y, a random variable N is Poisson distributed with rate = y. 1. Determine marginal distribution of N. 2. Evaluate expectation of N. 3. Derive variance of N.
gem505Lv10
22 Jan 2023
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