Question

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

Z	3	2	1	0	−1
P(Z)	0.3	0.2	0.4	0	0.05

Answer 1

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

1. 0 ≤ p_i ≤ 1
2. ∑p_i = 1

Z	3	2	1	0	−1
P(Z)	0.3	0.2	0.4	0	0.05

 Here ∑p_i = 0.3 + 0.2 + 0.4 + 0 + 0.05

= 0.95 ≠ 1

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

Answer 2

Here, p_i ≥ 0, `AA` i = 1, 2, ...., 5

Now consider,

`sum_("i" = 1)^5 "P"_"i"` = 0.3 + 0.2 + 0.4 + 0 + 0.05

= 0.95 ≠ 1

∴ Given distribution is not p.m.f.