A problem about E(x|x>y)

Joe Zhang · science forum beginner Joined: 10 Dec 2005 Posts: 12

I met a problem which was to calculate the mean of x given that x > y.
Both x and y are normal random variables, but they may have different
mean and variance. Besides, they are independent.

Let us use mx, sx and my, sy to represent their mean and standard
deviation, respectively. I formulate E(x|x>y) as follows:

E(x|x>y) = constant * \int_{x=-\infty}^{\infty} \int_{y=-\infty}^{x}
x * exp( -(x-mx)^2/2sx^2 ) * exp( -(y-my)^2/2*sy^2 ) dx dy

It turns out that the double integral can be simplified only when mx =
0. Since it looks like a very general problem in mathematics, I was
wondering if there is any method to solve the problem completely. Or,
is it a known function which can only be evaluated by numerical methods?

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