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Math Help - How can I compute E[max Xi \ X1<X2<X3]?

  1. #1
    kui
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    How can I compute E[max Xi \ X1<X2<X3]?

    If Xi , i = 1, 2, 3, are independent exponential random variables with rate lambda_i, i=1, 2, 3 find E[max Xi \ X1<X2<X3] ,

    How can I proof that the answer is (1/lambda1+lambda2+lambda3)+(1/lambda2+lambda3)+(1/lambda3)
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  2. #2
    MHF Contributor matheagle's Avatar
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    From what you've written I think you want the expected value of the largest order statistic
    from a sample of size three from an exponential distribution.
    If that's true, you should find the density of that order stat then integrate.
    Nope, I was wrong. Your random variables have different parameters.
    But you can still derive the density of the largest of these three.
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  3. #3
    Moo
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    Hello,
    Quote Originally Posted by kui View Post
    E[max Xi \ X1<X2<X3]
    What is this notation ?
    Thanks ^^
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