Equation XXXXXXXXXXgives f Si (s i |N(t)=n), which is the density of random variable Si conditional on N(t) = n for n i. Multiply this expression by Pr{N(t) = n} and sum over n to find f Si (s i );...

Equation (2.42) gives f_Si(s_i|N(t)=n), which is the density of random variable Si conditional on N(t) = n for n i. Multiply this expression by Pr{N(t) = n} and sum over n to find f_Si(s_i); verify that your answer is indeed the Erlang density.