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February 22nd, 2011, 03:58 PM   #1
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Uniform distribution of Random variables

Hi, I have a question:
Let X1,X2,...Xn be independent random variables, each having a uniform distribution over (0,1). Let M= max (X1,X2,...,Xn). Show that the distribution function of M, FM(*), is given by FM(x)=x^n. 0<=X<=1.

So I have no problem figuring out the majority part of it, and I worked up to FM(x) = P(X1<=x)*P(X2<=x)*...P(Xn<=x). But I have trouble finding the individual P. However, a friend told me that since it's uniformly distributed from 0 to 1, P(X1<=x)...P(Xn<=x) are each x. But I am still confused at how do you get x? Thanks!
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February 23rd, 2011, 01:11 PM   #2
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Re: Uniform distribution of Random variables

Uniform between 0 and 1 means that the density function = 1 for 0<x<1 and 0 otherwise. Therefore the distribution function is the integral from 0 to x (for x in the range (0,1) of 1.
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