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

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

Z 3 2 1 0 −1
P(Z) 0.3 0.2 0.4 0 0.05
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Solution 1

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

  1. 0 ≤ pi ≤ 1
  2. ∑pi = 1
Z 3 2 1 0 −1
P(Z) 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(Z) cannot be regarded as p.m.f. of the random variable Z.

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.

Concept: Probability Distribution of Discrete Random Variables
  Is there an error in this question or solution?
Chapter 7: Probability Distributions - Exercise 7.1 [Page 232]

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