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Question
A die is thrown three times. Let X be 'the number of twos seen'. Find the expectation of X.
Solution
\[\text{ We have } , \]
\[p = \text{ probability of getting a number two in a throw } = \frac{1}{6} \text{ and } \]
\[q = 1 - p = 1 - \frac{1}{6} = \frac{5}{6}\]
\[\text{ As, X denote 'the number of twos seen } ' . \]
\[\text{ So, X follows binomial distribution with parameters n = 3 and } p = \frac{1}{6}\]
\[ \therefore E\left( X \right) = np = 3 \times \frac{1}{6} = \frac{1}{2}\]
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