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We have N i.i.d random variables from the uniform distribution between 0 and 1. If N=1,...

We have N i.i.d random variables from the uniform distribution between 0 and 1. If N=1, what is the probability that the nth order statistic is less than or equal to the value x? (In other words, what is Pr(X(n)1≤x)?)

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Answer #1

You say that there are N iid random variables and next N=1.

Hence there is only one random variable

So nth order statistics is same as the original random variable.

So P(X(n)<=x) = P(X<=x)=x, 0<x<1

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