Questn -7.5

please can anyone elaborate what exactly the solution is??

 

Hi

I think the solution to 7.5 does show the entire computation. Which part is not clear?

Hint: Recall E[Exponential RV] & E[Poisson RV] from the notes and re-look at the solution!

 

how come E[X|K=k]=k,
i mean if we go by the definition of expectation ?

 

In the question it states, that given K = k, X follows a Poisson(k) distribution.
Mean of a Poisson rv is equal to its parameter value.

So, E[X| K = k] = k