Question

A player tosses two coins. He wins ₹10 if 2 heads appear, ₹5 if one head appears, and ₹2 if no head appears. Then variance of winning amount is ______.

• A. 38.5
• B. 8.25
• C. 5.5
• D. 44.00

Hint:

Always organize random variable problems into a clean table with columns for $x$, $P(x)$, $x \cdot P(x)$, and $x^2 \cdot P(x)$. Summing the last two columns instantly gives you the required components for the variance formula.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Variance $V(X) = E(X^2) - [E(X)]^2$. First, find the probability for each winning amount.

Step 2: Formula Application:
Sample space: $\{HH, HT, TH, TT\}$. $P(10) = 1/4$ (2 heads); $P(5) = 2/4 = 1/2$ (1 head); $P(2) = 1/4$ (0 heads).

Step 3: Explanation:
$E(X) = (10 \cdot 1/4) + (5 \cdot 1/2) + (2 \cdot 1/4) = 2.5 + 2.5 + 0.5 = 5.5$. $E(X^2) = (10^2 \cdot 1/4) + (5^2 \cdot 1/2) + (2^2 \cdot 1/4) = 25 + 12.5 + 1 = 38.5$. $V(X) = 38.5 - (5.5)^2 = 38.5 - 30.25 = 8.25$.

Step 4: Final Answer:
The variance is 8.25.