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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 |
Solution 1
P.m.f. of random variable should satisfy the following conditions :
(a) 0 ≤ pi ≤1
(b) ∑pi = 1
| X | 0 | 1 | 2 |
| P(X) | 0.4 | 0.4 | 0.2 |
(a) Here 0 ≤ pi ≤1
(b) ∑pi = 0.4 + 0.4 + 0.2 = 1
Hence, P(X) can be regarded as p.m.f. of the random variable X.
Solution 2
Here, pi > 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.
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