Gate2017 ss Q55

0. For any discrete random variable X, with probability mass function

P(X = j) = p_j, p_j ≥ 0, j ∈ {0,....N} and

, define the polynomial function

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

Answer
Comment
Array

Option : B
Explanation :
Derivative of g_x(z) evaluated at z=1 gives expectation E(X) of X.
Therefore, take derivative of gY(z) with respect to z, and plug in z=1
Derivative is N.β.(1 - β + βz)(N-1), plug in z=1, gives Nβ.

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