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(Solved): Loss model, Actuarial science (show formulas and steps) ( 6 marks) The amount (in hundreds) x_(1) ...
Loss model, Actuarial science (show formulas and steps) ( 6 marks) The amount (in hundreds)
x_(1),x_(2),dots,x_(6)were paid on a motor insurance liability claim. The amount of a single payment has the single Pareto distribution
f(x|\theta )=(a\theta ^(\alpha ))/(x^(\alpha +1)), with ,\alpha =2,\theta in[a,b].Consider a prior distribution of
\pi (\theta )=(1)/(\theta ). (A) (1 mark) Determine the model distribution. (B) (1 mark) Determine the joint distribution. (C) (2 marks) Determine the marginal distribution. (D) (2 marks) Determine the posterior distribution.
