mobius0
07-16-2009, 11:08 PM
Let X1...Xn be independent, identically, distributed random variables. Determine the cumulative distribution functions of X(k),n, the kth largest of n observations. Compute the pdf in the case n=5, k=4 when X1...X5 are standard uniform random variables.
What I have attempted:
Set X(k),n, = kth largest
summation from j=k to n (Prob(X(j-1)<a and X(j)>a)
Using the cdf and binomial theorem I got
summation from j=k to n NCJ (1-Fx(a))^j (Fx(a))^n-j
I know this can't be right.. Where am I going wrong?
Thanks.
What I have attempted:
Set X(k),n, = kth largest
summation from j=k to n (Prob(X(j-1)<a and X(j)>a)
Using the cdf and binomial theorem I got
summation from j=k to n NCJ (1-Fx(a))^j (Fx(a))^n-j
I know this can't be right.. Where am I going wrong?
Thanks.