Binomial And Multinomial Theorem. X y n xn r 0 n r xryn r combinatorial interpretations. Proceed by induction on m.
Proceed by induction on m. The sum is taken over all combinations of nonnegative integer indices k 1 through k m such that the sum of all k i is n. In statistics the corresponding multinomial series appears in the multinomial distribution which is a generalization of the binomial distribution.
According to the theorem it is possible to expand the polynomial x y n into a sum involving terms of the form ax b y c where the exponents b and c are nonnegative integers with b c n and the coefficient a of each term is a specific positive integer depending on n and b.
N r n n r special cases. 8 07 math 3012 at the georgia institute of technology 210 subscribers. N r represents 1. In statistics the corresponding multinomial series appears in the multinomial distribution which is a generalization of the binomial distribution.
