May 00 #18 .

[Crazycow]

Can any1 help me wif this? The question looks real simple. Tried to do it using 1st & 2nd moment , but consistently get bad answer.

Esitmate A: E(uA)= 1000 sd(uA)= 400
Estimate B: E(uB)= 1200 sd(uB)= 200

Estimate C is a weighted avg of the 2 esitmates A & B

uC = w. uA +(1-w).uB

Determine the value of w that minimise sd (uC).

I mean I understand the solution but I dont understand why using 1 & 2 moments dont work.

[Surfohio]

It works for me to use 1st and 2nd moments, but I end up with the same equation as in the solution, Var(C) = w^2 Var(A) + (1-w)^2 Var(B)

[Abraham Weishaus]

Perhaps you misunderstood the problem and calculated it as a mixture? This is a weighted sum of random variables, so the second moment is

You'd then use independence to factor the second summand, and use the facts given. This is the hard way to do the problem, though.

[Crazycow]

I did read it as a mixture distribution. Thx

[Wendy Crewson]

I get confused about how to tell the difference between a weighted sum of random variables and a mixture. There is an example in Mahler's notes in the simulation section where he tries to make the distinction, but it is not clear to me. Is it just a matter of being told whether we are dealing with a weighted sum versus a mixture?? Any thoughts would be appreciated. Keep in touch.

[Abraham Weishaus]

If random variables are added, that's a sum (weights don't have to add up to 1). If distribution functions (F) or density functions (f) are added together (with weights adding up to 1), that's a mixture.

[Crazycow]

Dr Abe, u r leet.