Fall 1998 question 25

Rich Sieger ( (no email) )
Mon, 25 Oct 1999 08:34:05 -0700

f(x) =3D 0.5 (1/lambda_1) exp(-x/lambda_1) + 0.5 (1/lambda_2) exp(-x/lambda=
_2)=20

Mean =3D 1, variance =3D k

If k is 3/2, determine method of moments estimate of lambda_1

I tried this (I'll use L for Lambda):

Mean =3D 1 =3D 0.5 (L1 + L2) =3D=3D> L2 =3D 2-L1

Second moment =3D 1^2 +k =3D .5 [2(L1)^2 +2(L2)^2]

since k =3D 3/2, substituting L2 =3D 2-1, I get

second moment 1.75 =3D L1^2 + (2-L1)^2 =3D L1^2 + 4 - 4L1 + L1^2

or 0 =3D L1^2 - 2 L1 + 1.125

getting the roots, L1 =3D [2+/- sqrt(4- 4(1.125) ]/2, which is an =
irrational number.

What am I doing wrong?

Rich Sieger

richsieger@cnico.com