GATE ME 2024 Set 1 — Question 44
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Engineering Mathematics → Probability → Expectation & Moments
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Question
Let be a continuous random variable defined on such that its probability density function for and otherwise. Let . Then the expected value of is_____. (rounded off to 2 decimal places)
Correct answer
0.38 to 0.39
Solution
Given that is a continuous random variable with a probability density function (PDF) for . This indicates that follows a continuous uniform distribution, .We are asked to find the expected value of . By the law of the unconscious statistician (LOTUS), the expected value is given by:Substituting and for :To solve this integral, we can use the substitution , which implies . The limits of integration change from to :Using the standard integral :Since :Using the value :Rounding to two decimal places, we get . The official GATE answer key allows a range of to .
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