Hello,
When you're differentiating the first integral, the constant is when u=t, and the part to be differentiated is when u=0.
This would rather give
and since is the pdf of an exponential, . But as to get , I don't know, sorry...
Let be the size of the nth generation in an age-dependent branching process , the lifetime distribution of which is exponential with parameter . If , show that the probability generating function of satisfies
i get:
from a theorem:
differentiating with respect to t
however i am not sure this right as the Generating functions are confusing and i am uncertain as where to go next.
Hello,
When you're differentiating the first integral, the constant is when u=t, and the part to be differentiated is when u=0.
This would rather give
and since is the pdf of an exponential, . But as to get , I don't know, sorry...