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