Actuarial Outpost ASM Manual. Exercise 51.1.
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#1
02-09-2018, 12:33 AM
 tcd Member Non-Actuary Join Date: Nov 2015 Posts: 38
ASM Manual. Exercise 51.1.

Hi,

I don't know whether it is forbidden or not to write out the question here so I will just give a general description.

This problem asks for Buhlman probability. There are two dice, each with different numbers. You are told one dice is selected from the pair and rolled 4 times. You are told the result of its first three rolls and asked for the expected value of the 4th.

The solution mechanically works through the Buhlman steps. EPV and VHM using both dices etc.

However the dices have different numbers. So you know that the selected dice has to be dice A.

It seems like a trick question to me, but it's actually not. Or am I misunderstanding the question?
#2
02-09-2018, 12:44 AM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,339

First the die is the singular and dice is the plural. Don't know the specifics of the problem but it could be illustrating the difference between the Bayes and Buhlman estimates.
#3
02-09-2018, 02:40 AM
 tcd Member Non-Actuary Join Date: Nov 2015 Posts: 38

I'll paraphrase

Two fair dice from which you pick one.
First is numbered 1,2,3,4,5,6
Second is numbered 6,7,8,9,10,11

The chosen dice is rolled four times times and you are told that the first three rolls get 1,2,3

Using Buhlman, What is expected value for fourth roll?

(I use dice rather than die. I also used "dices" above which was incorrect but I did that just to prevent confusion. Die is used more in US English. )

The answer is 2.538 which in itself seems suspicious...........you basically are almost assuming that rolling the dice is a non-Markovian process. I mean you know for certain which of them it is. And you are saying that the expected value of the next roll is less because the first three rolls were low...I guess maybe what you are updating is the assumption that it is fair i.e. each one is uniformly distributed......

Last edited by tcd; 02-09-2018 at 11:21 AM..
#4
02-09-2018, 03:59 PM
 Abraham Weishaus Member SOA AAA Join Date: Oct 2001 Posts: 7,197

Buhlmann is an approximation, and has mechanical steps. It ignores the actual distributions and only uses their means and variances. Even though you know the exact distributions in this case, you don't use them.

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