Number 24

cooksec@nationwide.com
Mon, 10 May 1999 08:17:41 -0400

Here's a poser...I just got my test back and missed this one. I've seen Stuart
Klugman's posted solution and can follow it. What I'm confused about is why my
approach is invalid. Stuart used Buhlmann's approach; I went the Bayesian
route.

This is the baseball player question. The number of errors is Poisson with mean
theta and theta is Gamma (alpha, beta).

We know alpha/beta = 1/10 and alpha/(beta)^2 = 1/400. This gives alpha=2
and beta=20.

With 1 error in 60 games (observations), I took the posterior distribution
of theta to be Gamma with alpha=3 and beta=80.

The mean of the posterior, and the Bayesian estimate (since we have a
Gamma-Poisson pair) is 3/80=.0375.

With 60 more games, the expected number of errors is 2.25, answer B.

So what's wrong with this approach?

Chris