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Problem 1: 15 points (= 5 + 5 + 5] Assume that a discrete random variable (N) is geometrically distributed, with P[N 2 n] = (-1)' for n = 0, 1, .... An n OT Given N = n, a random variable (Y) has conditional distribution with density, pYIN (y\n) = .3.'.ev for y>0. 1. Determine the marginal density of Y. 2. Show that for any natural r, the moment EY'] is finite and evaluate it. 3. Derive variance of Y, that is Var [Y] = E [Y2) – (E [Y])?
Problem 1: 15 points (= 5 + 5 + 5] Assume that a discrete random variable (N) is geometrically distributed, with P[N 2 n] = (-1)' for n = 0, 1, .... An n OT Given N = n, a random variable (Y) has conditional distribution with density, pYIN (y\n) = .3.'.ev for y>0. 1. Determine the marginal density of Y. 2. Show that for any natural r, the moment EY'] is finite and evaluate it. 3. Derive variance of Y, that is Var [Y] = E [Y2) – (E [Y])?
gem505Lv10
22 Jan 2023
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