Say we are given 2 well-defined (very large N) probabilty density functions: P1 and P2, with means mu1 & mu2 and SDs sigma1 & sigma2.

What is the probability that a randomly selected sample from P1 will be greater than a random sample from P2??


How would the confidence in our answer change if we knew the distributions were normal but our sample size was much smaller?

Any help is appreciated. Thanks