1. 

   Molly Ton up Member

   Hi Guys,
   
   What is the distribution of N is this question? i would have assumed poisson, but the mean and var arent the same once we have computed them from the conditional formulae
   
   Thanks
   Molly

    

   Molly, Sep 16, 2022

   #1
2. 

   Andrew Martin ActEd Tutor Staff Member

   Hi Molly
   
   N is a Poisson RV but the parameter is treated as a random variable. So:
   
   N | mu = a ~ Poi(a)
   or
   N | mu ~ Poi(mu)
   
   The unconditional moments (eg E[N] = E[E[N| mu]] can be calculated using the formulae on page 16 of the Tables.
   
   Hope this helps
   
   Andy

    

   Andrew Martin, Sep 17, 2022

   #2

   Molly likes this.

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