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    How to find P(x1<x2)




    X2 and x1 being 2 independent exponential variables with mean 5 and 2.
    I found f(x1) and f(x2) and defined y as x2 - x1 but I'm stuck there. How do I calculate f(y)? or is there another way of finding P(x1<x2).
    Thank you!

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    Re: How to find P(x1<x2)

    Just doing the integration directly shouldn't be too bad for this problem.
    I don't have emotions and sometimes that makes me very sad.

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    Re: How to find P(x1<x2)

    Thanks but if I knew what to integrate I wouldn't have posted the question!

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    Re: How to find P(x1<x2)

    Do you know the joint distribution? Can you draw out the region the defines where x1 < x2?
    I don't have emotions and sometimes that makes me very sad.

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    Re: How to find P(x1<x2)

    @Dason. No I don't know the joint distribution

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    Re: How to find P(x1<x2)

    The joint distribution of independent random variables is just the product of their corresponding pdfs.
    I don't have emotions and sometimes that makes me very sad.

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    Re: How to find P(x1<x2)

    I did not do it with the joint function. I integrated f(x1) from 0 to x2 and subtracted the result from 1.
    I was wondering if I should have used y=x1-x2 instead and solve P(y>0)

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    Re: How to find P(x1<x2)


    Quote Originally Posted by statgoon13 View Post
    I did not do it with the joint function. I integrated f(x1) from 0 to x2 and subtracted the result from 1.
    How does that get you the answer? Wouldn't that be a function of x2 still?
    I was wondering if I should have used y=x1-x2 instead and solve P(y>0)
    That is one way to do it but it isn't nearly as easy as the method I mentioned earlier.
    I don't have emotions and sometimes that makes me very sad.

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