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.

(i) Given: E(X) = 2.94

We know that, μ = E(X)







[given: E(X) = 2.94]


⇒ 2.94 × 50 = 69 + 26A


⇒ 147 – 69 = 26A


⇒ 78 = 26A



⇒ A = 3


(ii) We know that,


Var(X) = E(X2) – [E(X)]2


= ΣX2P(X) – [Σ{XP(X)}]2


= ΣX2P(X) – (2.94)2


Firstly, we find ΣX2P(X)






=19.06


Now, Var(X) = 19.06 – (2.94)2


= 19.06 – 8.6436


= 10.4164

50