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Bivariate expected value and variance

  1. Nov 26, 2011 #1
    1. The problem statement, all variables and given/known data

    I need to know these formulas to answer the homework problems, but I can't squeeze the forumlas out of the gibberish in the book, so I'm asking for varification of the formulas.

    For a bivariate probablity density function, for example f(x,y)= 2xy when x and y are between 0 and 3, and 0 elsewhere,

    expected value of x: E[X]
    expected value of (X,Y)
    Variance of x: Var[X]
    Var[X,Y]


    [tex] E[x] = \int_{-\infty }^{\infty }xf_1(x) \: \mathrm{d}x [/tex] where [itex] f_1(x) [/itex] is the marginal probability distribution of x. Is this correct?

    Now, for E[X,Y], do you think the book means the expected value of the product XY? because the only formula it gives here is for the product. So, E[XY]. If they really mean E[X,Y] and not E[XY], then is there a formula for E[X,Y]? I don't have one in my book.

    As for Var[X], is it [tex] Var[x] = \int_{-\infty }^{\infty }x^2f_1(x) \: \mathrm{d}x -(E[x])^2 [/tex] ?

    And for Var[X,Y], I have no idea, the only formulas I see in my book are for Var[X+Y].

    Remember, these are all for bivariate distributions.
     
  2. jcsd
  3. Nov 26, 2011 #2

    I like Serena

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    Homework Helper

    E[X,Y] would be (E[X],E[Y]).
    Same for Var[X,Y].

    You have the right E[X] and Var[X].
     
  4. Nov 26, 2011 #3
    Thanks
     
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