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Math Help - Help calculating covariance. thank you for your help

  1. #1
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    Question Help calculating covariance. thank you for your help

    3.) Let X and Y be continuous random variables with joint density function
    f(x,y)=\left\{\begin{array}{lr}(8/3)(x)&0\le x \le 1, x\le y \le 2x\\0&otherwise\end{array}\right.

    How would you calculate the covariance/correlation coefficient with those bounds? thank you for your help.
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  2. #2
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    If X ranges from 0 to 1, and the bounds of Y are defined in terms of X, you should be able to determine what the bounds of Y are.
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  3. #3
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    Quote Originally Posted by matheagle View Post
    I don't follow.
    We require students to know calc3 before taking prob/stats.
    Wild. Must be different pre-reqs throughout the country. Calc 1 is pretty much it for most Stats classes at the Universities/Colleges here. It's not until you're deep in upper division Stat classes that a full compliment of Calc is required; definitely not for lower division stat courses.
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  4. #4
    MHF Contributor matheagle's Avatar
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    This is basic calc 3.
    YOU must draw the region.
    First draw the lines y=x, y=2x and x=1.
    Then find the three vertices, (0,0), (1,1) and (1,2).
    This rectangle is easier to integrate via dydx than dxdy.
    Once you have the bounds the three integrals are all the same except for the integrand.

    E(XY) =\int_0^1 \int_x^{2x}xyf(x,y)dydx

    E(X) =\int_0^1 \int_x^{2x}xf(x,y)dydx

    E(Y) =\int_0^1 \int_x^{2x}yf(x,y)dydx

    IT's better to look at this two dimensionally and NOT obtain the marginals.
    Obtaining the marginals forces you to do a particular order of integration
    and I prefer dydx in all three cases in this example.

    Likewise

    E(X^2) =\int_0^1 \int_x^{2x}x^2f(x,y)dydx

    E(Y^2) =\int_0^1 \int_x^{2x}y^2f(x,y)dydx
    Last edited by matheagle; November 18th 2009 at 12:27 AM.
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  5. #5
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    I still don't know why Calc 1 is a minimum requirement for a class that uses elements from Calc 3. While it may be basic, more than a few people have actually been exposed to it yet.
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  6. #6
    MHF Contributor matheagle's Avatar
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    I don't follow.
    We require students to know calc3 before taking prob/stats.
    We also do change of variables that require jacobians from calc3.
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