My Math Forum Uniform distribution of Random variables

 February 22nd, 2011, 03:58 PM #1 Member   Joined: Sep 2007 Posts: 49 Thanks: 0 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!
 February 23rd, 2011, 01:11 PM #2 Global Moderator   Joined: May 2007 Posts: 6,834 Thanks: 733 Re: Uniform distribution of Random variables Uniform between 0 and 1 means that the density function = 1 for 0

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# let X1, X2, ... Xn be independent random variables, each having a uniform distribution over (0,1). Let M = maximum. Show that the distribution function of M is given by Fm(x)-xn what is

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