GATE EC 2014 Set 1 — Question 15
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Engineering Mathematics → Probability → Joint Probability
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Question
Let and be independent and identically distributed random variables with the uniform distribution on . The probability is ________
Correct answer
0.32 to 0.34
Solution
Since and are independent and identically distributed (i.i.d.) continuous random variables, the probability of any one of them being the largest is equal due to symmetry.Let be the event that is the largest, be the event that is the largest, and be the event that is the largest. Because the variables are continuous, the probability of a tie (e.g., ) is zero. Thus:By symmetry:Therefore:Alternatively, using integration:Since they are i.i.d. , and for .
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