# Question 26 you are given 1 the prior distribution

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Question 26You are given:(1)The prior distribution for the parameter O is inverse exponential with parameter 2.(ii)Given 0 = B,claim sizes follow a gamma distribution with parametersa= 2 and BClaim amounts 1 and 2 are observed for the first two claims.Which of the following is the posterior distribution of 0 ?.AGamma with parametersa=6,8=Gamma with parametersa=5, B=Inverse gamma with parametersa =5, 8=Inverse gamma with parametersa =6, B=5B5C5D5Exam CQuestions - Chapter 9
ESingle parameter Pareto witha =5,0 = 2BPP Professional Education: Summer/Fall 2012Page 13
Question 27You are given:(1)The number of claims isPoisson(.)(ii) The prior distribution for2 isa gamma(2,0.20) distribution(iii)A random sample of claims numbers gives the values:0010102200Determine the Bayesian estimate for2assuming a squared-error loss function.BCDEQuestions - Chapter 9Exam C
Question 28You are given:(i)Claim numbers have aPoisson(,)distribution(ii)The following prior distribution is to beused for2: TI-(2)=0.6[5e-52]+0.4 [1002e-1022 >(iii)During the last year, two claims were received. Determine theBayesian estimate for2assuming a squared-error loss function.],0
B0.46C0.47D0.48E0.49Page 14© BPP Professional Education: Summer/Fall 2012
Question29You are given the following information about 4 dice:DiceProbability of throwing a six1-21/631/241/10A dice is chosen at random, and the following sequence of results is obtained, where "1" indicatesthat a six is thrown, and "0" indicates that a six is not thrown:{Xi, X2,X3} = {0,0,1}Determine the expected value ofX4 IS ,whereX4 isthe next result for the same dice.
Question 30You are given:Policies in a portfolio can produce either 0,1 or 2 claims in a year.For each policy, the number of claims in a year has the distribution:Number of claims012Probability2q0.6-g0.4 -( i i i ) T h e pr i o r d en s i ty fo rqi s :A-(q)=156.25q3,0q(iv) A policy from the portfolio produced one claim last year.Determine the Bayesian estimate of the number of claims next year from the same policy.g.4Abetween 0.40 and 0.45between 0.45 and 0.50between 0.50 and .55between 0.55 and 0.60BCD

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Term
Spring
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Tags
Probability theory, BPP Professional Education, claim amount