A discrete random variable X takes the values 0, 1, 2, 3, 4 and its mean is 1.6. If P(X = 1) = 0.4, P(X = 4) = P(X = 2) and P(X = 3) = 2 P(X = 2), then P(X = 0) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) - 0.2
$\text{Let } P(X=2)=p$
$P(X=4)=p,\;\; P(X=3)=2p,\;\; P(X=1)=0.4$
$P(X=0)=1-(0.4+p+2p+p)=0.6-4p$
$E(X)=1.6$
$0\cdot P(X=0)+1(0.4)+2p+3(2p)+4p=1.6$
$0.4+2p+6p+4p=1.6$
$0.4+12p=1.6$
$12p=1.2 \Rightarrow p=0.1$
$P(X=0)=0.6-4(0.1)=0.2$
$P(X=0)=0.2$