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Q and A Bank 2. Questions 2.13 and 2.14

M

mcallist

Member
Hi All,

Could someone please help me with these issues?

Q2.13
I would find it v hard in an exam to notice that this could be rewritten as a NBin distribution. Are we expected to be able to recognise this, and if so, is there something easy that I'm missing? If it's not hassle, could someone share the intermediate steps please?

The distribution given in the question is P(N = n) = 9(n+1)4^-n-2 and it's rewritten as (n+1 choose n)(3/4)^2(1/4)^n

Q2.14
How can we tell if we're meant to use a Type 1 or Type 2 Negative Binomial for this from the info in the question(Just says Negative Binomial)

Thanks a lot,
Tom
 
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Q2.13
There are mainly three types of Compound distribution given in ch.7 - Compound poisson, compound binomial and Compound negative binomial distribution. I think we can recognize the pdf of N given in the qus. keeping in mind these distributions. In this qus., it neither seems pdf of a poisson dist. nor its a binomial. So, we can get an idea that it may be negative binomial dist. Then we can compare the given pdf from the discrete dist. pdfs from the tables (N is always discrete). Then we have to rearrange the pdf according to that given in the tables.

Q2.14
I think, they always take Type-2 neg. binomial in subject CT6. If you see, page 28 of ch.7, it is written that its type-2 version when compound neg. binomial dist. is introduced. And also, I think it may be because in type-2, X starts from 0 i.e. x=0,1,2,3,4.... and we have this dist. for random variable N i.e. no. of claims, minimum value of which may be zero.

This is what I can think for both of your queries, if it seems sensible to you.
 
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