ENG EC 381 Lecture Notes - Lecture 4: Binomial Theorem, Binomial Coefficient, Binomial Distribution

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The binomial theorem (or binomial expansion) describes the algebraic expansion of power of a binomial. According to theorem, it is possible to expand the power n b c y. The coefficient a in the term of ax known as the binomial coefficient. c is y. If we perform an experiment consisting of multiple identical sub experiment, it is often a responsible model to assure the sub experience are independents: we call the sub experiment: independent trials. Consider {fc , f} where p[fc] = p and p[f] = 1 p are the outcomes of sub experiments. Consider one outcome in e. eo = { s, s, s, s, f, f, f, f} where number of successes is k. P[eo] = p k (1 p) n-k. P[e] = (# of sequences with k successes). p k (1 p) n-k. =( ) p k ( 1 p) n-k ( a binomial probability )

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