Chapter 10, Example 10.8 - Independent samples

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.

 

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..