RE: Fall 1998 question 25
Christopher So ( (no email) )
Mon, 25 Oct 1999 12:25:04 -0400
On October 25, 1999 11:34 AM, Rich Sieger [SMTP:RichSieger@cnico.com] wrote:
> f(x) = 0.5 (1/lambda_1) exp(-x/lambda_1) + 0.5 (1/lambda_2) exp(-x/lambda_2)
>
> Mean = 1, variance = k
>
> If k is 3/2, determine method of moments estimate of lambda_1
>
> I tried this (I'll use L for Lambda):
>
> Mean = 1 = 0.5 (L1 + L2) ==> L2 = 2-L1
>
> Second moment = 1^2 +k = .5 [2(L1)^2 +2(L2)^2]
>
> since k = 3/2, substituting L2 = 2-1, I get
>
> second moment 1.75 = L1^2 + (2-L1)^2 = L1^2 + 4 - 4L1 + L1^2
Should it be 2.5 instead of 1.75??
>
> or 0 = L1^2 - 2 L1 + 1.125
>
> getting the roots, L1 = [2+/- sqrt(4- 4(1.125) ]/2, which is an irrational number.
>
> What am I doing wrong?
>
> Rich Sieger
>
> richsieger@cnico.com
>
>