1. The number of claims in a month for a portfolio of insurance
policies is thought to follow the Negative-binomial distribution
with pdf
?(?) =( Γ(20+?) / Γ(? +1)Γ(20) ) . ?^20 . (1−?)^?, ? =
0,1,2,…
A sample of 4 months had claim numbers of 15, 25, 20 and 21.
a) There is no prior information for p. Using an uninformative
prior to derive the posterior distribution for p. [12 marks]
b) Show that the mode of the Beta...