Question

A random variable $X$ takes the values $0,1,2,3$ and its mean is$1.3$. If $P(X=3)=2P(X=1)$ and $P(X=2)=0.3$ , then $P(X=0)=$

• A. $0.1$
• B. $0.2$
• C. $0.3$
• D. $0.4$

Answer 1

The correct option is D $0.4$

$E\left[X\right]={\sum }_{i=0}^3{x}_i{p}_i=0\ast P(X=0)+1\ast P(X=1)+2\ast P(X=2)+3\ast P(X=3)=1.31\ast P(X=1)+2\ast 0.3+3\ast 2\ast P(X=1)=1.3P(X=1)=0.1Nowusing{\sum }_{i=0}^3{p}_i=1=P(X=0)+P(X=1)+P(X=2)+P(X=3)P(X=0)+0.1+0.3+0.2=1P(X=0)=0.4$