Question

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.

Answer 1

(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