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Question
An unbiased coin is tossed 4 times. Find the mean and variance of the number of heads obtained.
Solution
\[\text{ We have } , \]
\[p = \text{ probability of getting a head in a toss } = \frac{1}{2}, \]
\[q = \text{ probability of getting a tail in a toss } = \frac{1}{2}\]
\[\text{ Let X denote a success of getting a head in a toss . Then } , \]
\[\text{ X follows binomial distribution with parameters n = 4 and } p = \frac{1}{2}\]
\[ \therefore \text{ Mean } , E\left( X \right) = np = 4 \times \frac{1}{2} = 2\]
\[\text{ Also, variance, Var } \left( X \right) = npq = 4 \times \frac{1}{2} \times \frac{1}{2} = 1\]
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