A coin is tossed twice and outcomes are recorded. If the random variable X represents the number of heads in the experiment, then the expectation of X will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1
The four equally likely outcomes are HH, HT, TH, TT, so X takes the values 0, 1, 2 with
\( \displaystyle P(X = 0) = \frac{1}{4},\quad P(X = 1) = \frac{2}{4},\quad P(X = 2) = \frac{1}{4} \)
The expectation is \(E(X) = \sum x\,P(x)\):
\( \displaystyle E(X) = 0\cdot\frac{1}{4} + 1\cdot\frac{2}{4} + 2\cdot\frac{1}{4} = \frac{4}{4} = 1 \)
Shortcut: X is binomial with n = 2 and \(p = \frac{1}{2}\), so \(E(X) = np = 2 \times \frac{1}{2} = 1\).
CBSE Applied Mathematics (Class XII):
Mathematical Expectation of Discrete Probability Distribution
