Let X1, X2, X3, X4, X5 be independent continuous random variables having a common cdf F...

Let X1, X2, X3, X4, X5 be independent continuous random variables having a common cdf F and pdf f, and set p=P(X1 <X2 <X3 < X4 < X5).

(i) Show that p does not depend on F. Hint: Write I as a five-dimensional integral and make the change of variables ui = F(xi), i = 1,··· ,5.

(ii) Evaluate p.
(iii) Give an intuitive explanation for your answer to (ii).

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milcah answered 2 months ago

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