= Solution
The ratio of <expected process variance> to <variance of hypothetical means> is $K=s^2/v=(\alpha+1)/(k-2)$, and the <credibility factor> is $Z=n/(n+K)$. Holding $\alpha,\lambda$ fixed, an increase in $k$ decreases $K$. Hence \b[the <credibility factor> increases], approaching one as $k$ tends to infinity. Extending the formula to real $k>2$ makes the sign explicit:
$$
\frac{\partial Z}{\partial k}=\frac{n(\alpha+1)}{[n(k-2)+\alpha+1]^2}>0.
$$
For the integer values in the model this establishes the same strict monotonicity. The collective claim <expected value> $m=\alpha/[\lambda(k-1)]$ also changes, but the conclusion concerns the relative weight of experience: conditional noise declines faster than the variation of the risk means.
Back to article page
