## sleung one year 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

what does mean E(X2i) means E(even) ?

2. sleung

It means $E(X _{i}^{2})$ Sorry about the notation - it didn't copy and paste correctly.

3. mahmit2012

oh got

4. mahmit2012

so S is sigma(i)=1100Xi is it right

5. mahmit2012

|dw:1392444372176:dw|

6. mahmit2012

but it is not the answer because the problem wants var(s) but i dont know what is exact s?

7. sleung

Sorry, $S=\sum_{i=1}^{100}X _{i}$

8. mahmit2012

|dw:1392445311784:dw|

9. mahmit2012

|dw:1392445440041:dw|

10. mahmit2012

|dw:1392445541588:dw|

11. sleung

I can't see the right side of what you did.

12. sleung

How'd you get n^2-n?

13. sleung

|dw:1392447809874:dw| How'd you get this part?

14. mahmit2012

all is n^2 so you have to subtract from n (x1 x2 .. xn)

15. mahmit2012

all term in sigma without itself terms

16. sleung

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.