GATE EE 2021 Set 1 — Question 37
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Engineering Mathematics → Probability → Expectation & Variance
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Question
Suppose the probability that a coin toss shows "head" is , where . The coin is tossed repeatedly until the first "head" appears. The expected number of tosses required is
Correct answer
(C) 1 / p
Solution
Let be the random variable representing the number of tosses until the first head appears. This follows a geometric distribution with success probability .
The probability mass function is for
The expected value is given by:
where
Using the identity
Alternatively, using the recursive property of expectation:
Correct option is (C).
The probability mass function is for
The expected value is given by:
where
Using the identity
Alternatively, using the recursive property of expectation:
Correct option is (C).
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