I'm given this problem. σ²(t) = V((1-t)X + tY) = at² + 2bt+c where

a=? b=? c=?

E(X) = 2

E(Y) = 3

E(X^2) = 53

E(Y^2) = 45

E(XY) = -21

Can someone please explain what σ²(t) = V((1-t)X + tY) means and how to solve it?

Thanks.

Printable View

- February 21st 2008, 07:47 AMtaypezStatistics Question
I'm given this problem. σ²(t) = V((1-t)X + tY) = at² + 2bt+c where

a=? b=? c=?

E(X) = 2

E(Y) = 3

E(X^2) = 53

E(Y^2) = 45

E(XY) = -21

Can someone please explain what σ²(t) = V((1-t)X + tY) means and how to solve it?

Thanks. - February 21st 2008, 08:06 AMheathrowjohnny
I think is the variance and it is equaled to . This is for one random variable .

But for two random variables.

But then there are the terms. So plug in and to solve for . So for , . For , . - February 21st 2008, 08:19 AMtaypez
Alright, does this make any sense...

I calculated:

cov(X,Y) = -27

V(X) = 49

V(Y) = 54

so, for: at^2 + 2bt + c

a = V(x)= 49

b = cov(X,Y) = -27

c = V(Y) = 54

I'm not sure that what he's looking for.

Then how would I find the value of t* that minimizes this? t* = -σy/σx