Recent content by chili237

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    Calculating the Joint PMF of Two Independent Poisson Random Variables

    I'm completely new to probability, so I'm learning as I go. The convolution theorem isn't something I know or have in any of my materials, but I'll do some research and hopefully that'll point me in the right direction.
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    Calculating the Joint PMF of Two Independent Poisson Random Variables

    X~Pois(λ)=> px(k)=e-λλk/k! Y~Pois(μ)=> py(k)=e-μμk/k! Find pX,X+Y(k,n)=P(X=k, X+Y=n) ...I know the pmf for X+Y ~ Pois(λ+μ) As I understand the joint pmf for two independent random variables would be the product of the two individual pmfs. However as X+Y is dependent on X I got really...
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    Finding the Joint PMF of Two Independent Poisson Random Variables

    Homework Statement X~Pois(λ)=> px(k)=e-λλk/k! Y~Pois(μ)=> py(k)=e-μμk/k! Find pX,X+Y(k,n)=P(X=k, X+Y=n) Homework Equations ...I know the pmf for X+Y ~ Pois(λ+μ) The Attempt at a Solution As I understand the joint pmf for two independent random variables would be the product of the two...