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When was N. R. Pathak born?
N. R. Pathak was born on 1915-09-30.
Prove that nCr plus nCr minus 1 equals n plus 1Cr?
nCr + nCr-1 = n!/[r!(n-r)!] + n!/[(r-1)!(n-r+1)!] = n!/[(r-1)!(n-r)!]*{1/r + 1/n-r+1} = n!/[(r-1)!(n-r)!]*{[(n-r+1) + r]/[r*(n-r+1)]} = n!/[(r-1)!(n-r)!]*{(n+1)/r*(n-r+1)]} = (n+1)!/[r!(n+1-r)!] = n+1Cr
What is the difference between a permutation and combination?
n p =n!/(n-r)! r and n c =n!/r!(n-r)! r
Why is it said that poisson distribution is a limiting case of binomial distribution?
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.
How many groups of 20 can you choose out of 23?
Combinations of r from n without replacement is c(n,r) = n!/(n-r)!r! c(n,r) = 23!/20!3! c(n,r) = 1771.
General formulae for the combination nCr in terms of n and r?
nCr=n!/(r!(n-r)!)
What is ncr value?
n(n-r)/r
When did Theodore N. Ely die?
Theodore N. Ely died in 1915.
When did Tim N. Machin die?
Tim N. Machin died in 1915.
When was Paul N. Yu born?
Paul N. Yu was born in 1915.
When was Joseph R. Wood born?
Joseph R. Wood was born in 1915.
When was R. J. Unstead born?
R. J. Unstead was born in 1915.
