60% members of a committee favour a certain proposal and 40% members oppose the proposal. A member is selected and let the random variable $X = 0$ if he opposes and $X = 1$ if he is in favour. Then the variance of the random variable X is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\frac{6}{25}$ **
Given probabilities:
$P(X = 1) = 0.6$, $P(X = 0) = 0.4$
Mean:
$E(X) = (1)(0.6) + (0)(0.4) = 0.6$
Variance formula for a Bernoulli random variable:
$Var(X) = p(1 - p)$
Here, $p = 0.6$
$Var(X) = 0.6(1 - 0.6) = 0.6(0.4) = 0.24$
Variance of X = 0.24 = 24/100 =6/25