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प्रश्न
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 |
उत्तर १
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.
उत्तर २
Here, pi > 0, `AA` i = 1, 2, 3
Now consider,
`sum_("i" = 1)^3 "P"_"i"` = 0.6 + 0.1 + 0.2
= 0.9 ≠ 1
∴ Given distribution is not p.m.f.
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