# Thread: Another difficult Gaussian integral

1. ## Another difficult Gaussian integral

Hello all,

This time, I'm trying to compute

where are the standard Gaussian pdf and cdf. The parameters a, b, and c are arbitrary constants.

I noticed some other threads on difficult Gaussian integrals, but this one has the added issue of these parameters. I am trying to apply the technique from the other thread -- could somebody please let me know if I'm on the right track? I write

where . This is where , yielding an answer of .

2. ## Re: Another difficult Gaussian integral

Originally Posted by sven svenson
Hello all,

This time, I'm trying to compute

where are the standard Gaussian pdf and cdf. The parameters a, b, and c are arbitrary constants.

Yes, your solution looks good to me.

Note that it is a good idea for you to specify the conditions on what values the constant terms can take (for obvious reasons).

3. ## Re: Another difficult Gaussian integral

Can you elaborate a bit on why the integral in the second equation (a probability times a pdf) gives the probability P(X <= Y)? It just is not sinking in why this is so.

4. ## Re: Another difficult Gaussian integral

It is just law of total probability. (in a continuous version)

Here the random variable is independent of

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts