GATE EC 2024 Set 1 — Question 33
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Engineering Mathematics → Probability → Joint Probability
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Question
Suppose and are independent and identically distributed random variables that are distributed uniformly in the interval . The probability that is __________.
Correct answer
0.5 to 0.5
Solution
Since and are independent and identically distributed uniform random variables in , their joint probability density function (PDF) is for and . The probability can be found by integrating the joint PDF over the region where within the unit square . This region is a triangle with vertices , , and . The area of this region is . Since the total area of the sample space (unit square) is , the probability is .
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