Question

A fair coin is tossed twice and outcomes are noted. If the random variable \( X \) represents the number of heads that appeared in the experiment, then the mathematical expectation of \( X \) is:

• A. \( 1 \)
• B. \( \frac{1}{2} \)
• C. \( \frac{1}{4} \)
• D. \( \frac{3}{2} \)

Hint:

The expectation of a random variable is calculated as \( E(X) = \sum X \cdot P(X) \), where \( P(X) \) is the probability of \( X \).

Answer 1

The Correct Option is A

Step 1: The possible outcomes for two tosses of a fair coin are: \( HH, HT, TH, TT \). The corresponding values of \( X \) (number of heads) are \( 2, 1, 1, 0 \). 
Step 2: Calculate the expectation \( E(X) \): \[ E(X) = \sum X \cdot P(X) = 2 \cdot \frac{1}{4} + 1 \cdot \frac{2}{4} + 0 \cdot \frac{1}{4} = 1. \]