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Relating probability distributions huh?

  1. May 7, 2010 #1
    1. The problem statement, all variables and given/known data

    Problem description:
    A variable X has expected value 0.002 in meters. Consider X - 0.002, scale to millimeter, and we get Y.

    a) Express Y as a function of X
    b) Relate the probability distributions FX and FY
    c) Relate the probability density functions fX and fY

    2. Relevant equations

    [tex] F(x) = \operatorname P ( X \leq x ) = \int_{-\infty}^x f(t) \, \mathrm{d}t [/tex]

    [tex] \int_{-\infty}^{\infty} f(x) \, \mathrm{d}x = 1[/tex]

    [tex] f(x) = F'(x) \geq 0 [/tex]

    3. The attempt at a solution

    a) Y = 1000X - 2
    (I think)

    b) I have no clue. I mean, I could make a wild guess, but I don't see any reason to.

    c) I suppose we get fX and fY by differentiating FX and FY... somehow.

    I also don't really know what it means to "relate" these things. Is it to express the one in terms of the other, so that for example if a*b = c then relating a to b I either say that a = c/b or that b = c/a? Or what?
    Last edited: May 7, 2010
  2. jcsd
  3. May 7, 2010 #2


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    Gold Member

    That looks good.

    Start by looking at the cumulative distribution function for Y:

    [tex]G(y) = P(Y\le y) = P(1000 X - 2 \le y) = P(X \le\ ??)\ ...[/tex]

    You should be able to calculate this in terms of fX and it's derivative with respect to y will give you the density function for y.
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