Introduction
Poisson distribution evolved from two distribution.
Two distribution that is, if the coin positive upward probability of p, toss n times coins, this n times the coin toward the K-time (k<=n) probability of
P (k) =CKNPK (1−p) n−k (1) p (k) = C_n^kp^k (1-p) ^{n-k} \ \ \ \ \ \ \ \ \ \ (1)
the expectation of the coin upward is:
E (k) =PN (2) e (k) = pn \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2)
If we think of expectations as a constant value λ\ \lambda\. That is: Now I can according to the size of N to control p \ p \, that is, n \ n \ The larger, p \ p\ the smaller the number of coins facing the expectation of the same (constant for λ\ \lambda\):
E (k) =pn=λ (3) e (k) = pn= \lambda \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
OK, this is the end of the primer, the following begins the formal deduction ...
derivation of Poisson distribution
⨂12⨂34 \sideset{^1_2}{^3_4}\bigotimes⨂12⨂34 \sideset{^1_2}{^3_4}\bigotimes⨂12⨂
