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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 |

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#### Solution 1

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.

#### Solution 2

Here, p_{i} > 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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