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

Correct option is A

Given
P(X=3)=2P(X=1) and P(X=2)=0.3
Let
P(X=1)=k
=>P(X=3)=2k
Mean =0×P(0)+1×P(1)+2×P(2)+3×P(3)
1.3=k+2×0.3+6k
k=1/10=0.1
Now
P(X=0)+P(X=1)+P(X=2)+P(X=3)=1
P(X=0)+0.1+0.3+0.2=1
P(X=0) +0.6 =1
P(X=0)=0.4