For any discrete random variable X, with probability mass function P(X = j) = p j , p j ≥ 0, j ∈ {0,….,N}, and \sum ↙\stackrel{N}{j = 0}⁡p_{j} = 1, define the polynomial function g_{x} (z) = \:\sum ↙\stackrel{N}{j = 0}⁡p_{j}z^{j}. For a certain discrete random variable Y, there exists a scalar β ∈ [0, 1] such that g γ (z) = (1 - β + β z) N . The expectation of Y is

Not expressible in terms of N and β alone

GATE Computer Science (CS) 2017 Shift 2 Solved Paper

Question : 41 of 65

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For any discrete random variable X, with probability mass function P(X = j) = p_j, p_j ≥ 0, j ∈ {0,….,N}, and

∑ ↙{j = 0}↖{N}⁡p_{j} = 1

, define the polynomial function

g_{x} (z) = \:∑ ↙{j = 0}↖{N}⁡p_{j}z^{j}

. For a certain discrete random variable Y, there exists a scalar β ∈ [0, 1] such that g_γ (z) = (1 - β + β z)^N. The expectation of Y is

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