Question

State if the following is not the probability mass function of a random variable. Give reasons for your answer.

X	0	1	2	3	4
P(X)	0.1	0.5	0.2	− 0.1	0.2

Answer 1

P.m.f. of random variable should satisfy the following conditions :

(a) 0 ≤ p_i ≤ 1

(b) ∑p_i = 1

X	0	1	2	3	4
P(X)	0.1	0.5	0.2	− 0.1	0.2

P(X = 3) = − 0.1, i.e. p_i < 0 which does not satisfy 0 ≤ p_i ≤ 1

Hence, P(X) cannot be regarded as p.m.f. of the random variable X.

Answer 2

Here, P(X = 3) = – 0.1 < 0

∴ Given distribution is not p.m.f