Question

Let X be a discrete random variable whose probability distribution is defined as follows: where k is a constant. Calculate (i) the value of k (ii) E (X) (iii) Standard deviation of X. Select the correct answer from above options

Answer 1

(i) the value of k We know that, Sum of the probabilities = 1 ⇒ k = 0.02 (ii) To find: E(X) The probability distribution of X is: Therefore, μ = E(X) (iii) To find: Standard deviation of X We know that, Var(X) = E(X2) – [E(X)]2 = ΣX2P(X) – [Σ{XP(X)}]2 = [2k + 12k + 36k + 80k + 250k + 432k + 686k +0] – [5.2]2 = 1498k – 27.04 = 29.96 – 27.04 = 2.92 We know that, standard deviation of X = √Var(X) = √2.92 = 1.7088 ≅ 1.7