Chapter 8 Section 4

Chapter 8 Section 4 - Bernoulli Trials

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Bernoulli Trials http://www.math.wichita.edu/history/topics/probability.html#bern-trials Boy? Girl? Heads? Tails? Win? Lose? Do any of these  sound familiar? When there is the possibility of  only two  outcomes  occuring during any single event, it is called a  Bernoulli Trial.  Jakob Bernoulli , a profound  mathematician of the late 1600s, from a family of  mathematicians, spent 20 years of his life studying  probability. During this study, he arrived at an equation  that calculates probability in a Bernoulli Trial. His proofs  are published in his 1713 book  Ars Conjectandi  (Art of  Conjecturing). 
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Jacob Bernoulli: Hofmann sums up Jacob Bernoulli's contributions as follows:-  Bernoulli greatly advanced algebra, the infinitesimal calculus,  the  calculus of variations , mechanics, the theory of series, and  the theory of  probability.  He was self-willed, obstinate,  aggressive, vindictive, beset by feelings of inferiority, and yet  firmly convinced of his own abilities. With these characteristics,  he necessarily had to collide with his similarly disposed brother.  He nevertheless exerted the most lasting influence on the  latter.   Bernoulli was one of the most significant promoters of the  formal methods of higher analysis. Astuteness and elegance  are seldom found in his method of presentation and  expression, but there is a maximum of integrity
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What constitutes a Bernoulli Trial? http://www.math.wichita.edu/history/topics/probability.html#bern-trials To be considered a  Bernoulli trial , an experiment must meet each  of three criteria:  There must be  only 2 possible outcomes , such as: black or red,  sweet or sour. One of these outcomes is called a  success , and the  other a  failure . Successes and Failures are denoted as S and F,  though the terms given do not mean one outcome is more  desirable than the other.  Each outcome has a  fixed probability  of occurring; a success has  the probability of  p , and a failure has the probability of  1 - p Each experiment and result are completely  independent  of all  others. 
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Chapter 8 Section 4 - Bernoulli Trials

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