[(a/m)^(k-m)] * [(a^m)/m!] = (a^k)/[(m^m)*m!]
its part of a proof i need to learn for an exam on monday. i dont get it. surely it should be (a^k)/[(m^k-m)*m!] ?
That's what I get it to be too, eddie.
Unless we've both made the same mistake, which is unlikely, the equation is wrong.
Why did the vector cross the road?
It wanted to be normal.
Yes i get that too, the equation's wrong.
Student: "What's a corollary?"
Lecturer: "What's a corollary? It's like when a theorem has a child. And names it corollary."
ok, well i dont know if anyone will be able to help with this but i hope so.
it in my class notes for finding the steady state probability distribution of an M/M/m/n queue (erlang loss)
with arrival rate lamda and service time mu, for the second part of the proof, when m < k < n
P(k) = [lamda/(mu*m)] * P(k-1)
substituting a = lamda/mu
P(k) = (a/m) * P(k-1)
since we know k >= m that gives
P(k) = (a/m)^(k-m) * P(m)
and P(m) = [ a^m / m! ] *P (0)
which in my notes gives
P(k) = P(0) * (a^k)/[m^m * m!]
so there is something wrong somewhere, either in the proof or the formula at the end that we were trying to derive.