Iai May 2008

Hi ,
I have doubt in question paper of iai may 2008 q 15
and even i am unable to understand compound distribution what to consider S and N.by reading question how can one find out that it is compound distribution

 

Dvani

You are correct in stating that the question is confusing. It is one of the poorly drafted question I have ever seen.

Here, your S is actually X. Note, X can be written as Y(1) + ... + Y(N) where each Yi follows iid Bernoulli distribution with parameter 1/2.

N is said to follow the distribution with PMF f(n) = n/3, n = 1, 2.

You can now answer the question using the formulas given in the tables.

NB: In the solution there is a mistake. It starts with stating the PMF of X as Binomial. It is actually the PMF of X conditional on N.

 

Thank you it was really great help