Question
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(Z) $0.3$ $0.2$ $0.4$ $0$ $0.05$

Answer

P.m.f. of random variable should satisfy the following conditions:
  1. $0 \leq p_i \leq 1$
  2. $∑p_i = 1$
X $3$ $2$ $1$ $0$ $−1$
P(Z) $0.3$ $0.2$ $0.4$ $0$ $0.05$
Here $∑p_i = 0.3 + 0.2 + 0.4 + 0 + 0.05$
$= 0.95 \neq 1$
Hence, $P(Z)$ cannot be regarded as p.m.f. of the random variable $Z$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free