Question
State if the following is not the probability mass function of a random variable. Give reasons for your answer.
X $0$ $1$ $2$
P(X) $0.4$ $0.4$ $0.2$

Answer

P.m.f. of random variable should satisfy the following conditions :
(a) $0 \leq p_i \leq 1$​​​​​​​
(b) $∑p_i = 1$​​​​​​​
X $0$ $1$ $2$
P(X) $0.4$ $0.4$ $0.2$
(a) Here $0 ≤ p_i \leq 1$​​​​​​​
(b) $∑p_i = 0.4 + 0.4 + 0.2 = 1$
Hence, $P(X)$ can be regarded as p.m.f. of the random variable $X$.

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