Q.If a d.r.v. X takes values 0, 1, 2, 3, . . . which probability P (X = x) = k (x + 1)·5 −x, where k is a constant, then P (X = 0) = (A) 7/25
(B) 16/25
(C) 18/25
(D) 19/25

For a discrete random variable $X$ with possible values $x_1, x_2, x_3, \ldots$ occurring with probabilities $p_1, p_2, p_3, \ldots$, where $p_i = P[X = x_i]$, the rule that assigns each $x_i$ its probability $p_i$ is called the probability mass function of $X$, provided every $p_i \ge 0$ and the probabilities add up to 1, i.e. $\sum p_i = 1$. Listing the pairs $(x_i, p_i)$, often in a two-row table, gives the probability distribution of $X$. Every possible value must genuinely occur with positive probability, and because the values of $X$ between t …