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Chapter 10, Example 10.8 - Independent samples

T

trackr

Member
Hi guys,

I honestly don't understand how they are solving example 10.8. In the solution section - the first equation line after "the likelihood for these 15 low-risk & ....."

I thought it would be Product 1 to 48 and not Product 1 to 15. My thinking is the claims X (that ARISE from a low risk policy) have poi(mu) dist.

So:

X~Poi(mu) - since X is the claims and 15 low risk policies have 48 claims should it not be Product 1 to 48?

If anyone can explain this to me, I would be greatful!

Thanks!
 
Hi guys,

I honestly don't understand how they are solving example 10.8. In the solution section - the first equation line after "the likelihood for these 15 low-risk & ....."

I thought it would be Product 1 to 48 and not Product 1 to 15. My thinking is the claims X (that ARISE from a low risk policy) have poi(mu) dist.

So:

X~Poi(mu) - since X is the claims and 15 low risk policies have 48 claims should it not be Product 1 to 48?

If anyone can explain this to me, I would be greatful!

Thanks!
The number of claims, X, per year arising from a low-risk policy has a Poisson distribution with mean \( \mu \). And you'd use a sample of 15 low-risk policies to find the maximum likelihood.

say, you would find the maximum probability with average claims per policy for the samples to be actual. that's it.
 
Okay so I have been on this for like 4 hours. I am at my wit's end. (Side note: I honestly feel the notes should be a bit more explicit instead of just assuming we are all Harvard/MIT level genius.)

I think I understand a bit, but there is a bit more confusion.

Let me take it from the top:

X represents the total number of claims/ year from a Low risk policy (LRP). X~Poi(mu).
Similarly, Y represents the total number of claims/year from a HRP. Y~Poi(2 *mu).

Now there are 48 claims from 15 LRPs in a year. So lets say X = 48. So X ~ Poi(15*mu).
Similarly, there are 59 claims from 10 HRPs in a year. Therefore, Y~ Poi(10*2*mu).

Now,
L(mu)= (Prod 1st Policy to 15th Policy) [P(X=xi)] * (Prod 1st Policy to 10th Policy) [P(Y=yi)]

x(i) represents the number of claims for the i(th) policy. So sum of x(1) to x(15) = 48 (as there are 48 claims from 15 policies). Since now we are back to taking about an individual claim, the P(X=x(i))=Poisson prob func with mu as mean.

From there it is easy to follow the calculations.

I really hope before they jump into the solution, they spent some ink defining the variables.

If my thought process is wrong, please correct me.
 
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I guess you understand now,
But an error, you should not say, "Now there are 48 claims from 15 LRPs in a year. So lets say X = 48. So X ~ Poi(15*mu).
Similarly, there are 59 claims from 10 HRPs in a year. Therefore, Y~ Poi(10*2*mu)."(as from this you are changing definition of X & Y.)

PS: you can try Stats-Pack course notes before go on.:)
 
I guess you understand now,
But an error, you should not say, "Now there are 48 claims from 15 LRPs in a year. So lets say X = 48. So X ~ Poi(15*mu).
Similarly, there are 59 claims from 10 HRPs in a year. Therefore, Y~ Poi(10*2*mu)."(as from this you are changing definition of X & Y.)

PS: you can try Stats-Pack course notes before go on.:)

Could you please let me know which chapter in Stats Pack? I look through the stats pack now and then, but to be honest I could not find something that would help me with this? Thanks for your reply.
 
Mainly 'Random Variables'
then you shall not find notes as genius levels ;)

If you think that, 'it was rare event that you stuck in this kind of problems'... then it's normal..
 
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