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Answer by Iosif Pinelis for Expected size of binomial coefficient with...
Suppose that a real $c:=\lambda t>0$ and a natural $k$ are fixed, whereas $n:=N_0\to\infty$.Take any real $m>0$. Then$$f(k,t)=g_m(k,t)+h_m(k,t),$$where$$g_m(k,t):=e^{-c}\sum_{0\le...
View ArticleExpected size of binomial coefficient with Poisson arrivals?
I have a Poisson process where new elements arrive to a set with Poisson intensity $\lambda$. Initially, there are $N_0$ elements in the set. The probability that there are $N_0 + M$ elements in the...
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