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)	0.4	0.4	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
P(X)	0.4	0.4	0.2

(a) Here 0 ≤ p_i ≤1

(b) ∑p_i = 0.4 + 0.4 + 0.2 = 1

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

Answer 2

Here, p_i > 0, `AA`i = 1, 2, 3

Now consider,

`sum_("i" = 1)^3 "P"_"i"` = 0.4 + 0.4 + 0.2

= 1

∴ Given distribution is p.m.f.