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Question
Which of the following distributions of probabilities of a random variable X are the probability distributions?
(i)
| X : | 3 | 2 | 1 | 0 | −1 |
| P (X) : | 0.3 | 0.2 | 0.4 | 0.1 | 0.05 |
| X : | 0 | 1 | 2 |
| P (X) : | 0.6 | 0.4 | 0.2 |
(iii)
| X : | 0 | 1 | 2 | 3 | 4 |
| P (X) : | 0.1 | 0.5 | 0.2 | 0.1 | 0.1 |
(iv)
| X : | 0 | 1 | 2 | 3 |
| P (X) : | 0.3 | 0.2 | 0.4 | 0.1 |
Solution
(i) P (X = 3) + P (X = 2) + P (X = 1) + P (X = 0) + P (X = -1)
= 0.3 + 0.2 + 0.4 + 0.1 + 0.05
=1.05 > 1
It is not the probability distribution of random variable X.
(ii) P (X = 0) + P (X = 1) + P (X = 2)
= 0.6 + 0.4 + 0.2
= 1.2 > 1
It is not the probability distribution of random variable X.
(iii) P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4)
= 0.1 + 0.5 + 0.2 + 0.1 + 0.1
= 1
It is the probability distribution of random variable X.
(iv) P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)
= 0.3 + 0.2 + 0.4 + 0.1
= 1
It is the probability distribution of random variable X.
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