Suppose X1, ..., Xn are independent, identically distributed, purely continuous random variables, find P(X1<...<Xn).

Is the result the same if the random variables are not purely continuous?

In the purely continuous case, P(X1<...<Xn)=1/n! but there are innumerable examples for which the probability is smaller than 1/n!  when the random variables are not purely continuous.

Posted by Richard on 2006-08-23 16:21:51