6. The probability W(n) that an event characterized by a probability p occurs n times in N trials was shown by binomial distribution W(n) = Consider the situation where the probability p is small and n << N (a) Show that (1-p)N-ne-p (b) Show that N! (N − n)! (c) From (b) show it reduces to where X = Np ≈Nn N! n!(N − n)!P” (1 − p)N-n W(n)= = \n n! e et
6. The probability W(n) that an event characterized by a probability p occurs n times in N trials was shown by binomial distribution W(n) = Consider the situation where the probability p is small and n << N (a) Show that (1-p)N-ne-p (b) Show that N! (N − n)! (c) From (b) show it reduces to where X = Np ≈Nn N! n!(N − n)!P” (1 − p)N-n W(n)= = \n n! e et
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Transcribed Image Text:6. The probability W(n) that an event characterized by a probability p occurs n times in N trials was
shown by binomial distribution
N!
(N − n)!
(c) From (b) show it reduces to
W(n) =
Consider the situation where the probability p is small and n << N
(a) Show that (1-p)N-ne-p
(b) Show that
≈Nn
N!
n!(N − n)!P” (1 − p)N-n
W(n) =
=
where X = Np
(d) From (c), show that properly normalized
(e) Calculate the mean and variance
\n
n! e-t
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