Sum

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 ≤ p_{i} ≤ 1

**(b)** ∑p_{i }= 1

X |
0 | 1 | |||

P(X) |
0.1 | 0.5 | 0.2 | − 0.1 | 0.2 |

P(X = 3) = -0.1, i.e. p_{i} < 0 which does not satisfy 0 ≤ p_{i} ≤ 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

Is there an error in this question or solution?

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