Thread: Statistics 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.

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 , .

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