Question

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

X	0	-1	-2
P(X)	0.3	0.4	0.3

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
P(X)	0.3	0.4	0.3

(a)  Here 0 ≤ p_i ≤ 1

(b) ∑p_i = 0.3 + 0.4 + 0.3 = 1

Hence, P(X) can be regarded as p.m.f. of the random variable X.