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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 | 3 | 4 |
| P(X) | 0.1 | 0.5 | 0.2 | − 0.1 | 0.2 |
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Solution 1
P.m.f. of random variable should satisfy the following conditions :
(a) 0 ≤ pi ≤ 1
(b) ∑pi = 1
| X | 0 | 1 | 2 | 3 | 4 |
| P(X) | 0.1 | 0.5 | 0.2 | − 0.1 | 0.2 |
P(X = 3) = − 0.1, i.e. pi < 0 which does not satisfy 0 ≤ pi ≤ 1
Hence, P(X) cannot be regarded as p.m.f. of the random variable X.
Solution 2
Here, P(X = 3) = – 0.1 < 0
∴ Given distribution is not p.m.f
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