Choose the correct alternative : If p.m.f. of r.v.X is given below. x 0 1 2 P(x) q2 2pq p2 Then Var(X) = _______

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Since given data is p.m.f. of r.v. X, we get q2 + 2pq + p2 = 1 $\therefore$ (q + p)2 = 1 $\therefore$ (q + p) = 1 ...(i) E(X) = \sum\limits_{x=0}^{2} x\text{P}(x) = 0 x q2 + 1 x 2pq + 2 x p2 = 2pq + 2p2 = 2p (q + p) = 2p ...[From (i)] E(X2) = \sum\limits_{x=0}^{2} x^2\text{P}(x) = (0)2 x q2 + (1)2 x 2pq + (2)2 x p2 = 2pq + 4p2 $\therefore$ Var(X) = E(X2) – [E(X)]2 = 2pq + 4p2 – (2p)2 = 2pq + 4p2 – 4p2 = 2pq.

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