Given two normally distributed variables `x_1, x_2`

, is there a non-simulation method of calculating the probability that `x_1 > x_2`

?

Generalizing a bit, what is the probability that given a list of normally distributed variables `x_i`

, the probability that `x_a = max x_i`

?

jointnormal, in which case x_1-x_2 is normal. The second qu. asks if the set of joint normal rv's x_a-x_i are all positive, which is more difficult (requires some numerical integration, I think). – George Lowther May 10 '10 at 21:53