GATE EC 2018 Set 1 — Question 33
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Engineering Mathematics → Probability → Normal Distribution
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Question
Let and be independent normal random variables with zero mean and unit variance. The probability that is the smallest among the four is _______.
Correct answer
0.25 to 0.25
Solution
Since are independent and identically distributed (i.i.d.) continuous random variables, the probability that any one of them is the smallest is equal by symmetry.
There are 4 variables in total, and since they are i.i.d., each has an equal probability of being the minimum:Since the sum of these probabilities must be 1:
There are 4 variables in total, and since they are i.i.d., each has an equal probability of being the minimum:Since the sum of these probabilities must be 1:
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