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 :

0.24

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,

$E(X)=∑xP(X=x)$

$=0.P(X=0)+1.P(X=1)$

$=0.(0.6)^0(0.4)^1+(0.6)^1(0.4)^01$

$=0+0.6$

$=0.6$

$E(X^2)=∑x^2P(X=x)$

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

$=1×0.6=0.6$

$Var(X)=E(X^2)-(E(X))^2$

$=0.6-0.36$

$=0.24$