Patrick N. L. Bellinger died on 1962-05-30.
Patrick N. L. Bellinger was born on 1885-10-08.
L. N. Hardas died on 1939-01-12.
J. N. L. Baker died in 1971.
H. L. N. Salmon died on 1943-04-29.
John L. N. Stratton died on 1889-05-17.
N. Patrick Crooks was born on 1938-05-16.
Patrick N. Millsaps was born on 1973-03-16.
Patrick N. Hogan was born on 1979-02-15.
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This browser is totally bloody useless for mathematical display but...The probability function of the binomial distribution is P(X = r) = (nCr)*p^r*(1-p)^(n-r) where nCr =n!/[r!(n-r)!]Let n -> infinity while np = L, a constant, so that p = L/nthenP(X = r) = lim as n -> infinity of n*(n-1)*...*(n-k+1)/r! * (L/n)^r * (1 - L/n)^(n-r)= lim as n -> infinity of {n^r - O[(n)^(k-1)]}/r! * (L^r/n^r) * (1 - L/n)^(n-r)= lim as n -> infinity of 1/r! * (L^r) * (1 - L/n)^(n-r) (cancelling out n^r and removing O(n)^(r-1) as being insignificantly smaller than the denominator, n^r)= lim as n -> infinity of (L^r) / r! * (1 - L/n)^(n-r)Now lim n -> infinity of (1 - L/n)^n = e^(-L)and lim n -> infinity of (1 - L/n)^r = lim (1 - 0)^r = 1lim as n -> infinity of (1 - L/n)^(n-r) = e^(-L)So P(X = r) = L^r * e^(-L)/r! which is the probability function of the Poisson distribution with parameter L.
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If l > m and m > n then l > n by the transitive property of inequality.