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Math Help - Jointly distributed random variables

  1. #1
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    Jointly distributed random variables

    Hi can anyone help me with this q urgently
    Suppose that Y1 and Y2 are independent Poisson variables with means m1 and m2 respectively.
    Let X = Y1 + Y2. Show, using moment generating functions of independent variables or
    otherwise, that X has a Poisson distribution with mean m = m1+ m2.
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  2. #2
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    Quote Originally Posted by anitaK View Post
    Hi can anyone help me with this q urgently
    Suppose that Y1 and Y2 are independent Poisson variables with means m1 and m2 respectively.
    Let X = Y1 + Y2. Show, using moment generating functions of independent variables or
    otherwise, that X has a Poisson distribution with mean m = m1+ m2.
    You should know:

    1. m_X(t) = m_{Y_1}(t) \cdot m_{Y_2}(t) since Y1 and Y2 are independent random variables.

    2. m_{Y_1}(t) = e^{m_1 (e^t - 1)} and m_{Y_2}(t) = e^{m_2 (e^t - 1)}.

    It is simple to see that m_X(t) = e^{(m_1 + m_2) (e^t - 1)}.

    And since the moment generating function uniquely determines a probability distribution, ........
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