Question

A random variable $X$ takes values $-1,0,+1$. Its mean is $0.6$. If $P(X=0)=0.2$, then $P(X=1)=$

• A. $0.1$
• B. $0.3$
• C. $0.7$
• D. $0.6$

Answer 1

The correct option is C $0.7$

Let $P(X=1)=a,P(X=0)=b,P(X=-1)=c$,

We have,

$P(X=0)+P(X=1)+P(X=-1)=1$

$\Rightarrow 0.2+a+c=1$

$\Rightarrow a+c=0.8$....(i)

Also, mean = $\sum X.P\left(X\right)$

$\Rightarrow 0.6=a\times 1+0\times b+c\times (-1)$

$\Rightarrow a-c=0.6$ .....(ii)

From (i) and (ii) $a=0.7$ and $c=0.1$