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Math Help - Pretty basic probability question

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by Chuck37 View Post
    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.
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  3. #3
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    The variables are not necessarily zero mean.
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  4. #4
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    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)?
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  5. #5
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    Quote Originally Posted by Chuck37 View Post
    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.
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