sleung
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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mahmit2012
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what does mean E(X2i) means E(even) ?
sleung
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It means \[E(X _{i}^{2})\]
Sorry about the notation - it didn't copy and paste correctly.
mahmit2012
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oh got
mahmit2012
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so S is sigma(i)=1100Xi is it right
mahmit2012
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|dw:1392444372176:dw|
mahmit2012
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but it is not the answer because the problem wants var(s) but i dont know what is exact s?
sleung
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Sorry, \[S=\sum_{i=1}^{100}X _{i}\]
mahmit2012
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|dw:1392445311784:dw|
mahmit2012
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|dw:1392445440041:dw|
mahmit2012
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|dw:1392445541588:dw|
sleung
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I can't see the right side of what you did.
sleung
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How'd you get n^2-n?
sleung
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|dw:1392447809874:dw| How'd you get this part?
mahmit2012
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all is n^2 so you have to subtract from n (x1 x2 .. xn)
mahmit2012
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all term in sigma without itself terms
sleung
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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.