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Math Help - If X and Y are independent random variable...

  1. #1
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    If X and Y are independent random variable...

    Question : If X and Y are independent random variable with respective parameters \lambda_1 and \lambda_2
    Calculate
    i) P(X + Y = n)
    ii) P(x=k|X+Y= n)
    ----------------------------------------------------------------
    I cant understand what to do .....
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  2. #2
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    Quote Originally Posted by zorro View Post
    Question : If X and Y are independent random variable with respective parameters \lambda_1 and \lambda_2
    Calculate
    i) P(X + Y = n)
    ii) P(x=k|X+Y= n)
    ----------------------------------------------------------------
    I cant understand what to do .....
    The first thing you need to do is tell us what the distributions of X and Y are (exponential, I suppose)

    Nevertheless, no doubt somewhere in your notes there will be a theorem telling you what distribution X + Y follows when X and Y are independent.

    Now use the distributions of X, Y and X + Y to do the necessary calculations.

    Please show all your work if you're still stuck and need help.
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  3. #3
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    mR FANTASTIC
    i dont know which one to use but doesnt \lambda come in poisson

    and if i am correct if X and Y are independent the
    X+Y = Pr(X) + Pr(Y)

    please let me know what do u think about this
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  4. #4
    MHF Contributor matheagle's Avatar
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    yea this is a poisson and I proved this 2 weeks ago.
    Part b is a binomial that I proved here, twice.
    It took one minute to find it...
    http://www.mathhelpforum.com/math-he...tml#post420940
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    I went thrgh the post but i wasnt able to understand ......please could u provide me with an alternate way or explain me what have u done??
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  6. #6
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    Quote Originally Posted by zorro View Post
    I went thrgh the post but i wasnt able to understand ......please could u provide me with an alternate way or explain me what have u done??
    It would have helped if you said in your original post that the distributions were Poisson.

    The thread that has been quoted is detailed and complete. Unless there is something specific in it that you don't understand, you might have to accept that the question is beyond your current level of understanding.

    There is a lot of background material that you need to understand in order to be able to make sense of everything in the thread. It has been suggested before and now I will suggest again that you are advised to review all the work you are assumed to have covered in the several years leading up to the level you are currently studying at.
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  7. #7
    MHF Contributor matheagle's Avatar
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    I guessed Poisson by the lambda, but it couldn't have been exponential or any continuous distribution because of P(X=k|anything)=0.

    AND Zorro, you need to state the complete questions.
    You asked a hypothesis question today and no one can make a decision without alpha.
    We can obtain the p-value, but we can't decide on which hypothesis without the prob of making a type one error.
    Last edited by matheagle; January 1st 2010 at 06:24 AM.
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  8. #8
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    sorry and will keep in mind
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  9. #9
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    in the link provided how did he conclude that Pr(U|U+V=n) in my problem i have to prove that part ......i guess
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