I think in your solution you have second moment = 1.5 + 0.5^2 = 1.75.
That should do it.
-----Original Message-----
From: Rich Sieger [SMTP:RichSieger@cnico.com]
Sent: Monday, October 25, 1999 11:34 AM
To: studygroup4b@lists.casact.org
Subject: Fall 1998 question 25
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
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