Question

In a meeting 60\% of the members favour and 40\% oppose a certain proposal. A member is selected at random and we take $X = 0$ if he opposed and $X = 1$ if he is in favour, then $\text{Var}(X) =$

• A. $0.36$
• B. $0.24$
• C. $0.6$
• D. $0.06$

Hint:

Anytime a random variable is strictly defined as $1$ for an event happening and $0$ for it not happening, it is an Indicator (or Bernoulli) variable. You can bypass tables and immediately use $\text{Mean} = p$ and $\text{Variance} = p(1-p)$.

Answer 1

The Correct Option is B

Step 1: See this is a two value variable.
$X$ is 1 with chance $0.6$ and 0 with chance $0.4$. This is a Bernoulli case.

Step 2: Use the short formula.
For such a variable, $\text{Var}(X) = pq$.

Step 3: Compute.
$$\text{Var}(X) = 0.6 \times 0.4 = 0.24$$
\[ \boxed{0.24} \]