# State if the following is not the probability mass function of a random variable. Give reasons for your answer X 3 2 1 0 −1 P(X = x) 0.3 0.2 0.4 0 0.05 - Mathematics and Statistics

Sum

State if the following is not the probability mass function of a random variable. Give reasons for your answer

 X 3 2 1 0 −1 P(X = x) 0.3 0.2 0.4 0 0.05

#### Solution 1

P.m.f. of random variable should satisfy the following conditions :

(a) 0 ≤ pi ≤ 1

(b) ∑pi = 1.

 X 3 2 1 0 −1 P(X = x) 0.3 0.2 0.4 0 0.05

Here ∑pi = 0.3 + 0.2 + 0.4 + 0 + 0.05

= 0.95 ≠ 1

Hence, P(X) cannot be regarded as p.m.f. of the random variable X.

#### Solution 2

Here, pi ≥ 0, AA i = 1, 2, ...., 5

Now consider,

sum_("i" = 1)^5 "P"_"i" = 0.3 + 0.2 + 0.4 + 0 + 0.05

= 0.95 ≠ 1

∴ Given distribution is not p.m.f.

Is there an error in this question or solution?

#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 7 Probability Distributions
Exercise 7.1 | Q 3.4 | Page 232