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Math Help - [SOLVED] Sum of two Poissons

  1. #1
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    Question [SOLVED] Sum of two Poissons

    Suppose X has the poisson pmf pX(n) = λnexp(-λ)/n!, n>=0 and λ=5
    and Y has the poisson pmf
    pY(n)=μnexp(-μ)/n! n>=0 and μ=7
    Let Z=X+Y, find


    1. pz(7)
    2. Let A be the event that z=6. Find pY|A(4)
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  2. #2
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    Quote Originally Posted by essedra View Post
    Suppose X has the poisson pmf pX(n) = λnexp(-λ)/n!, n>=0 and λ=5
    and Y has the poisson pmf
    pY(n)=μnexp(-μ)/n! n>=0 and μ=7
    Let Z=X+Y, find


    1. pz(7)
    2. Let A be the event that z=6. Find pY|A(4)
    Are X and Y independent? If so, here's your starting point: Sum of two independent Poisson random variables
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  3. #3
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    I think they are independent but the point is, I don't know how to apply the formula.
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  4. #4
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    Quote Originally Posted by essedra View Post
    I think they are independent but the point is, I don't know how to apply the formula.
    Can you write down the pmf for Z? Where are you stuck with question 1?

    For question 2, what is
    pY|A(4)
    meant to mean?
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  5. #5
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    Quote Originally Posted by mr fantastic View Post
    Can you write down the pmf for Z? Where are you stuck with question 1?

    For question 2, what is

    meant to mean?
    Ok, I figured out.
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