Sheldon Ross 10: Exercise 3.96

Question: Consider a large population of families, and suppose that the number of children in the different families is independent Poisson random variables with mean λ. Show that the number of siblings of a randomly chosen child is also Poisson distributed with mean λ.


Analytical Solution

If you think about it, the first and the second sentence are basically talking about the same thing. Analytically, it can be proved as follows.

 


Simulation Solution

Looking at this in a database perspective, imagine that we have a table with three fields.


Code

 


End of the post 😉


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