Pretty basic probability question

• Mar 18th 2010, 08:48 AM
Chuck37
Pretty basic probability question
I feel kind of stupid, but I've wasted enough time, so...

Say I have three Gaussian random variables, a,b,c. What is Pr(a>b,a>c)?

The two things are not independent, so Pr(a>b,a>c)=Pr(a>b)*Pr(a>c|a>b).

Now I'm stuck on the conditional. Thanks for any help.

The real problem I want to solve is if I have N gaussians, what is the probability of a given one being bigger than all the rest. But one step at a time.
• Mar 18th 2010, 05:45 PM
awkward
Quote:

Originally Posted by Chuck37
I feel kind of stupid, but I've wasted enough time, so...

Say I have three Gaussian random variables, a,b,c. What is Pr(a>b,a>c)?

The two things are not independent, so Pr(a>b,a>c)=Pr(a>b)*Pr(a>c|a>b).

Now I'm stuck on the conditional. Thanks for any help.

The real problem I want to solve is if I have N gaussians, what is the probability of a given one being bigger than all the rest. But one step at a time.

Use symmetry. The probability that "a" is the greatest is 1/3.
• Mar 18th 2010, 06:00 PM
Chuck37
The variables are not necessarily zero mean.
• Mar 19th 2010, 12:53 PM
Chuck37
Maybe I'm being confusing. Say a is normal with mean 1 and std of 1, N(1,1), b is N(0,1) and c is N(0,1). What is pr(a>b, a>c)?
• Mar 19th 2010, 06:37 PM
awkward
Quote:

Originally Posted by Chuck37
Maybe I'm being confusing. Say a is normal with mean 1 and std of 1, N(1,1), b is N(0,1) and c is N(0,1). What is pr(a>b, a>c)?

Oops, I had jumped to the assumption that a, b, and c were independent and identically distributed variables. If they are not identically distributed then my previous remark does not apply, and the only way I know to find the answer to your question is to apply numerical methods to approximate the integral of the joint pdf of a, b, and c over the region where a is greater than b and c. I don't know how to evaluate the integral otherwise.