Set Loading. For example, it can calculate the likelihood of horse kicks killing three or more Prussian officers in a year. 52!≈0.
(
k
+
1
,
)
k
!
{\displaystyle {\frac {\Gamma (\lfloor k+1\rfloor ,\lambda )}{\lfloor k\rfloor !}}}
, or
e
i
=
0
k
i
i
!
{\displaystyle e^{-\lambda }\sum _{i=0}^{\lfloor k\rfloor }{\frac {\lambda ^{i}}{i!}}\ }
, or
Q
(
k
+
1
,
)
{\displaystyle Q(\lfloor k+1\rfloor ,\lambda )}
[
1
log
(
)
]
+
e
k
=
0
k
log
(
k
!
)
k
!
{\displaystyle \lambda [1-\log(\lambda )]+e^{-\lambda }\sum _{k=0}^{\infty }{\frac {\lambda ^{k}\log(k!)}{k!}}}
(for large
{\displaystyle \lambda }
)
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.
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.