Question

For the case where N is large,p is small, and the expectation is Np, a good approximation to the binomial function is P(m) =((λ^m)/m!)(exp(−λ)). This can be appropriate tothings like beta decay.

a) Show that it is normalized, i.e.∑P(m) = 1.(∑is o to infinity)

b) Show that the average value ofmis given by∑(mP(m) =λ.) (∑is o to infinity) (Hint: take aλout of the sum and show that the sum can be rewritten to look like the sumyou used in part a).)

c) Show that the variance is given byσ2=∑((m−λ)2P(m) =λ.) (∑is o to infinity).

Answer 1