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