The Probability mass functions of Random variable X is :
$P(X=x) = (0.6)^x(0.4)^{1-x}; x=0, 1 $ The variance of X is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0.24
The probability mass function (PMF) of the random variable X is,
$P(X=x)=(0.6)^x(0.4)^{1-x}$
The expectation (Mean) of X is,
$E(X)=∑xP(X=x)$
$=0.P(X=0)+1.P(X=1)$
$=0.(0.6)^0(0.4)^1+(0.6)^1(0.4)^01$
$=0+0.6$
$=0.6$
$E(X^2)=∑x^2P(X=x)$
$=0^2P(X=0)+1^2P(X=1)$
$=1×0.6=0.6$
$Var(X)=E(X^2)-(E(X))^2$
$=0.6-0.36$
$=0.24$