GATE EC 2015 Set 3 — Question 37
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Engineering Mathematics → Probability → Expectation & Variance
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Question
A fair die with faces is thrown repeatedly till '3' is observed for the first time. Let denote the number of times the die is thrown. The expected value of is ______.
Correct answer
6 to 6
Solution
The random variable represents the number of trials until the first success in independent Bernoulli trials, where success is defined as rolling a '3'. This follows a geometric distribution with probability of success . The expected value of a geometric distribution is given by .
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