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Math Help - C.D.F

  1. #1
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    C.D.F

    Let X be a continuous random variable taking values in (a, b) with c.d.f. F, strictly increasing on (a, b). Show that Y = F(X) has a uniform distribution on (0, 1). How would you use a set of computer generated random numbers (assumed to be drawn form a uniform distribution on
    (0, 1) ), to simulate a random sample from

    f(x) = (1/a)e^(-x/a) ,x>0?

    I'm not quite sure how to do this, i'm fairly sure that the first bit is do with the fact that as it is strictly increasing there is a 1 to 1 mapping. I know that if i can show that P(Y<y)=y then i have demonstrated it but i'm not sure how?

    I have no idea how to start the second bit. Any hints would be greatly appreciated.

    Thanks.
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  2. #2
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    Quote Originally Posted by DeFacto View Post
    Let X be a continuous random variable taking values in (a, b) with c.d.f. F, strictly increasing on (a, b). Show that Y = F(X) has a uniform distribution on (0, 1). How would you use a set of computer generated random numbers (assumed to be drawn form a uniform distribution on
    (0, 1) ), to simulate a random sample from

    f(x) = (1/a)e^(-x/a) ,x>0?

    I'm not quite sure how to do this, i'm fairly sure that the first bit is do with the fact that as it is strictly increasing there is a 1 to 1 mapping. I know that if i can show that P(Y<y)=y then i have demonstrated it but i'm not sure how?

    I have no idea how to start the second bit. Any hints would be greatly appreciated.

    Thanks.
    Asked and answered here: http://www.mathhelpforum.com/math-he...functions.html

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