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After searching the net I found out that a solution to the problem is involved in the paper "Unified Analysis of Generalized Selection Combining with Normalized Threshold Test Per Branch", which deals with a telecommunication problem.
And it's not easy!!
Thanks for your replies!
Thanks for your reply!
The problem is the calculation of the probability that
a*min[ x1, x2,..., xn] > x1 + x2 +...+ xn.
If we consider the RV g=min[ x1, x2,..., xn], then its pdf will be
f_g(g)=n* f(g) ( 1-F(g) )^(n-1)
and its cdf
F_g(g)=1- ( 1-F(g) )^n
where f(x) and F(x) are the pdf and cdf of the RV x1, x2,..., xn.
Also, assume that f(x) is the pdf of the normal distribution.
Hi all,
I would appreciate any help regarding the following problem:
Consider the ordered random variables (R.Vs) x1 > x2 >, ...> xn. Each R.V is distributed according to the probability density function (pdf) f(x).
The question is: What is the probability that a*min[ x1, x2,..., xn] > x1 + x2 +...+ xn ?, where a is a real number greater than 1.
Sakes
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