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Math Help - pressing problem on probability functions

  1. #1
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    pressing problem on probability functions

    pls,help render a hand i solving this problem
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  2. #2
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    Quote Originally Posted by Usman View Post
    pls,help render a hand i solving this problem
    Please take the time to post the question rather than attaching it as a word document.

    The question is (more or less):

    X is distributed as a Poisson random variable with the usual pmf. Find the pmf of Y when:

    (a) Y = 4X
    (b) Y = X^2.

    ----------------------------------------------------------------------------------------------------------

    In each case the following theorem can be used:

    Suppose that X is a discrete random variable with pmf f(x). Let Y = u(X) define a one-to-one transformation between the value of X and the value of Y so that the equation y = u(u) can be uniquely solved for x in terms of y, x = v(y), say. Then the pmf of Y is g(y) = f(w(y)).

    Note that in (b) the necessary condition is satisfied because x \geq 0 \Rightarrow x = + \sqrt{y}. Also, (\sqrt{y})! is OK (why?).
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