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=1) and P(X=2) =0.3, then P(X-0), is

0.4

We have,

$P(X=0)+P(X=1)+P(X=2)+P(X=3) = 1$

and,

$0 × P(X=0)+ 1 × P(X=1) + 2 × P(X=2)+3 × P(X=3)=1.3$

$⇒ P(X+0) +3P(X=1)=0.7 $ and, $ 7P(X=1)=0.7$

$⇒ P(X=0)+3P(X=1)=0.7 $ and $ P(X=1)=0.1$

$⇒ P(X=0) = 0.4 $