Question

A random variable $X$ has the following probability mass function:

$X$	$-2$	$3$	$1$
$P(X=x)$	$\frac{\lambda }{6}$	$\frac{\lambda }{4}$	$\frac{\lambda }{12}$

Then the value of $\lambda$ is:

• A. $3$
• B. $1$
• C. $4$
• D. $2$

Answer 1

The correct option is D $2$

We know that sum of Probability mass function$=1$

$\sum P(X=x)=P(-2)+P\left(3\right)+P\left(1\right)$

$\Rightarrow 1=\frac{\lambda }{6}+\frac{\lambda }{4}+\frac{\lambda }{12}$

$\Rightarrow 1=\frac{2\lambda }{6}+\frac{3\lambda }{12}+\frac{\lambda }{12}$

$\Rightarrow \frac{2\lambda +3\lambda +\lambda }{12}=1$

$\Rightarrow 6\lambda =12$

$\therefore \lambda =\frac{12}{6}=2$