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sleung

  • 2 years ago

Okay, I have another one here: Suppose that X1,...,X100 are random variables with E(Xi)=100,E(X2i)=10100 If Cov(Xi,Xj)=−1,i≠j what is Var(S), where S=∑i=1100Xi ? I got Var(S) to be 100, which is the correct answer but what good does knowing the covariance do? I tried using it, and it just throws everything off.

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  1. mahmit2012
    • 2 years ago
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    what does mean E(X2i) means E(even) ?

  2. sleung
    • 2 years ago
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    It means \[E(X _{i}^{2})\] Sorry about the notation - it didn't copy and paste correctly.

  3. mahmit2012
    • 2 years ago
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    oh got

  4. mahmit2012
    • 2 years ago
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    so S is sigma(i)=1100Xi is it right

  5. mahmit2012
    • 2 years ago
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    |dw:1392444372176:dw|

  6. mahmit2012
    • 2 years ago
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    but it is not the answer because the problem wants var(s) but i dont know what is exact s?

  7. sleung
    • 2 years ago
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    Sorry, \[S=\sum_{i=1}^{100}X _{i}\]

  8. mahmit2012
    • 2 years ago
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    |dw:1392445311784:dw|

  9. mahmit2012
    • 2 years ago
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    |dw:1392445440041:dw|

  10. mahmit2012
    • 2 years ago
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    |dw:1392445541588:dw|

  11. sleung
    • 2 years ago
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    I can't see the right side of what you did.

  12. sleung
    • 2 years ago
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    How'd you get n^2-n?

  13. sleung
    • 2 years ago
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    |dw:1392447809874:dw| How'd you get this part?

  14. mahmit2012
    • 2 years ago
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    all is n^2 so you have to subtract from n (x1 x2 .. xn)

  15. mahmit2012
    • 2 years ago
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    all term in sigma without itself terms

  16. sleung
    • 2 years ago
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    Suppose that (X,Y) is uniformly chosen from the set given by \[0<X<3, x<y<\sqrt{3x} \]Find the marginal density of Y.

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