Question

The probability distribution of a discrete random variable $X$ is given below:

X	$2$	$3$	$4$	$5$
P(X)	$\frac{5}{k}$	$\frac{7}{k}$	$\frac{9}{k}$	$\frac{11}{k}$

The value of $k$ is

• A. $8$
• B. $16$
• C. $32$
• D. $48$

Answer 1

Answer: (C)

We have $\Sigma P\left(X\right) = 1$
$ \Rightarrow \frac{5}{k} + \frac{7}{k} +\frac{9}{ k} +\frac{11}{k} = 1$
$\Rightarrow \frac{32}{k}= 1$
$\Rightarrow k= 32$