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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) | 0.3 | 0.4 | 0.3 |

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#### Solution

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) | 0.3 | 0.4 | 0.3 |

(a) Here 0 ≤ p_{i }≤ 1

(b) ∑p_{i} = 0.3 + 0.4 + 0.3 = 1

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

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