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 Let X_{1}, X_{2}, … X_{n} be random variables,
We can use the CDF to find the CDF of the k^{th} largest of
these X. We call this X_{(k),} or the k^{th }order
statistic.
 The density for the min and max are special cases for k = 1 and k = n.
 If all the X_{i} are identical and independent, we can find the
density of the order statistics

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 P(X_{(k)} ~ (x, x+dx)) =
 P(one of the X’s in dx)*
 P(k1 of the X’s below x)*
 P(nk of the X’s above x)=
 P(one of the X’s in dx) P(nk of the X’s
above x)
 (P(X > x) =1 F(x))
 Number of ways to order X’s
P(k1 of the X’s below x)
 (P(X < x) = F(x))

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 When X_{i} are Unif(0,1) we obtain:
 f_{(k)}(x) =

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 Claim: If r=k and s=nk+1 are integers then:
 B(r,s) =

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 Definition: The p’th quantile of the distribution of a random variable X
is given by the number x such that
 P(X· x) = p.

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