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Math Help - probability distribution - quick question

  1. #1
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    probability distribution - quick question

    A variable Y \in [0..\infty) has probability density

    P(Y) = exp(-Y)

    I'm trying to find the probability distribution of U = 2Y + 5, so I have done:

     P_y(y) = P_x(h(y))\frac{dh}{dy}

     Y = h(U) = \frac{U - 5}{2} ; \frac{dh}{du} = \frac{1}{2}

    So  P(U) = \frac{1}{2} exp \frac{5 - U}{2}

    Could anyone please tell me if this is right or are probability density and probability distribution different things? I've looked up the defintions but I'm still confused.

    Thanks in advance!
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  2. #2
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    Quote Originally Posted by hunkydory19 View Post
    A variable Y \in [0..\infty) has probability density

    P(Y) = exp(-Y)

    I'm trying to find the probability distribution of U = 2Y + 5, so I have done:

     P_y(y) = P_x(h(y))\frac{dh}{dy}

     Y = h(U) = \frac{U - 5}{2} ; \frac{dh}{du} = \frac{1}{2}

    So  P(U) = \frac{1}{2} exp \frac{5 - U}{2}

    Could anyone please tell me if this is right or are probability density and probability distribution different things? I've looked up the defintions but I'm still confused.

    Thanks in advance!
    Your pdf for U is almost correct. It's

     P(U) = \frac{1}{2} exp \frac{5 - U}{2} for {\color{red}U \in [5..\infty)} and zero elsewhere.

    Actually, I'd use the notation f(u) = \frac{1}{2} exp \frac{5 - u}{2} for u \geq 5 and zero elsewhere.
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