Question

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

Y	−1	0	1
P(Y)	0.6	0.1	0.2

Answer 1

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

(a) 0 ≤ pi ≤ 1

(b) ∑pi = 1

Y	−1	0	1
P(Y)	0.6	0.1	0.2

Here ∑pi = 0.6 + 0.1 + 0.2

= 0.9 ≠ 1

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

Answer 2

Here, p_i > 0, ${\displaystyle \forall }$ i = 1, 2, 3

Now consider,

${\displaystyle \sum _{\text{i}=1}^3{\text{P}}_{\text{i}}}$ = 0.6 + 0.1 + 0.2

= 0.9 ≠ 1

∴ Given distribution is not p.m.f.