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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 - Mathematics and Statistics

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 ≤ pi ≤ 1

(b) ∑pi = 1

X 0 1      
P(X) 0.1 0.5 0.2 − 0.1 0.2

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