Question

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

• A. $0.2,0.8$
• B. $0.3,0.7$
• C. $0.7,0.1$
• D. $0.4,0.2$

Answer 1

The correct option is C $0.7,0.1$

We know $\sum P\left(X\right)=1\Rightarrow P(X=-1)+P(X=0)+P(X=1)=1\Rightarrow P(X=-1)+P(X=1)=0.8$ -----(i)

Given mean is $10.6$ $\Rightarrow (-1)\left(P\right(X=-1\left)\right)+\left(0\right)\left(P\right(X=0\left)\right)+1\left(P\right(X=1\left)\right)=0.6$

$\Rightarrow -P(X=-1)+P(X=1)=0.6$ ------(ii)

Adding (i) and (ii)

$2P(x=1)=1.4$

$P(x=1)=0.7$

$P(x=-1)=0.8-P(x=1)=0.8-0.7=0.1$

$\therefore P(X=-1)=0.1,P(X=1)=0.7$