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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 - Mathematics and Statistics

Sum

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, 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.

Is there an error in this question or solution?
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 7 Probability Distributions
Exercise 7.1 | Q 3.5 | Page 232
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