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The probability distribution of a discrete random variable X is given as under:

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The probability distribution of a discrete random variable X is given as under: Calculate: (i) The value of A if E(X) = 2.94 (ii) Variance of X. Select the correct answer from above options

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(i) We know that: (ii) Now, the distribution becomes E(X2) = 1 x ½ + 4 x 1/5 + 16 x 3/25 + 36 x 1/10 + 81 x 1/25 + 225 x 1/25 = ½ + 4/5 + 48/25 + 36/10 + 81/25 + 225/25 = 0.5 + 0.8 + 1.92 + 3.6 + 3.24 + 9 = 19.06 Variance (X) = E(X2) – [E(X)]2 = 19.06 – (2.94)2 = 19.06 – 8.64 = 10.42

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