GATE | GATE-CS-2017 (Set 2) | Question 59

(A) Nβ(1-β)
(B) Nβ
(C) N((1-β))
(D) Not expressible in terms of N and β

Answer: (B)
Explanation: g_y(z) = ((1- β) + βz)^N

Expanding  g_y(z) we’ll get binomial distribution  with n=N and p = β

Mean of binomial distribution is E[Y] = n*p = Nβ which seems to be the only correct option here.

Therefore, option B
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