# State whether the following is True or False : If p.m.f. of discrete r.v. X is x 0 1 2 P(X = x) q2 2pq p2 then E(x) = 2p. - Mathematics and Statistics

MCQ
True or False

State whether the following is True or False :

If p.m.f. of discrete r.v. X is

 x 0 1 2 P(X = x) q2 2pq p2

then E(x) = 2p.

• True

• False

#### Solution

Since given data is p.m.f. of r.v. X, we get
q2 + 2pq + p2 = 1
∴ (q + p)2 = 1
∴ (q + p) = 1                          ...(i)

E(X) = $\sum\limits_{x=0}^{2} x\text{P}(x)$

= 0 x q2 + 1 x 2pq + 2 x p2
= 2pq + 2p2
= 2p (q + p)
= 2p                  ...[From (i)]

E(X2) = $\sum\limits_{x=0}^{2} x^2\text{P}(x)$

= (0)2 x q2 + (1)2 x 2pq + (2)2 x p2
= 2pq + 4p2
∴ Var(X) = E(X2) – [E(X)]2
= 2pq + 4p2 – (2p)2
= 2pq + 4p2 – 4p2
= 2pq is True.

Is there an error in this question or solution?

#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Miscellaneous Exercise 8 | Q 3.04 | Page 154