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Bivariate expected value and variance

  • Thread starter ArcanaNoir
  • Start date
  • #1
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Homework Statement



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.
 

Answers and Replies

  • #2
I like Serena
Homework Helper
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E[X,Y] would be (E[X],E[Y]).
Same for Var[X,Y].

You have the right E[X] and Var[X].
 
  • #3
768
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Thanks
 

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