Question

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

• A. $0.7$
• B. $0.5$
• C. $0.1$
• D. $0.2$

Answer 1

The correct option is A $0.7$

$P\left(0\right)+P\left(1\right)+P(-1)=1$

$P\left(1\right)+P(-1)=1-0.2=0.8$ $\dots \left(i\right)$

$MeanValue=\sum x\left(i\right)\ast P\left(x\right(i\left)\right)$

$1\times P\left(1\right)+(-1)\times P(-1)+0=0.6$

$P\left(1\right)-P(-1)=0.6$

$P(-1)=P\left(1\right)-0.6$

substitute in $\left(i\right)$

$\Rightarrow P\left(1\right)+P\left(1\right)-0.6=0.8$

$\Rightarrow 2P\left(1\right)=1.4$

$\Rightarrow P\left(1\right)=0.7$