Question

Assertion(A) : A random variable $X$ takes the values $0,1,2.$ It's mean is $\mathrm{0.6.}$ If $P(X=0)=0.5,$ then $P(X=1)=0.4$

Reason(R) : $X:S\to R$ is a descreate random variable with range $\{X_1,X_2,X_3,\cdots \}$ then mean $=\sum _{r=1}^{\infty }{x}_{r}P(X=x_r)$

• A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
• B. Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
• C. $A$ is true but $R$ is false
• D. $A$ is false but $R$ is true

Answer 1

The correct option is A Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$

Let $P(X=1)=s,P(X=2)=t$

$X=x_i$	$0$	$1$	$2$
$P(X=x_i)$	$0.5$	$s$	$t$

So, $s+t=0.5,\mu =s+2t=0.6\left(\text{mean}\right)$
$\Rightarrow t=0.1,s=0.4\Rightarrow P(X=1)=0.4$