noob stat question

Nephi · science forum beginner Joined: 16 Jun 2006 Posts: 1

(If this is the wrong place to ask this forgive me.)

Suppose you randomly choose n numbers from some range (say 0 to 1). Call
the smallest one m. What is the expected value for m?

Thanks

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abose · science forum beginner Joined: 16 Jun 2006 Posts: 8

The CDF (Cumulative Distribution Function) of M is P(M<x)=P(M<all n
numbers)=x^n.
So PDF (density) of M is n*x^(n-1). This, incidentally, is Beta(n+1,1)
distribution.

So E(M)=Integrate[x*n*x^(n-1), {x,0,1}]=1/(1+n)

Nephi wrote:

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