7.2 Binomial Distribution.pdf - DATE MDM 4U1 LESSON NOTES...

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MDM 4U1 DATE: LESSON NOTES 7.2 Binomial Distributions Earlier We saw a sequence ot experments that depend On some chance clement. This is known as a stochastie process. A stochastic process is referred to as repeated trials if the exNperiments are identical. and the experiments are independent Examples of repeated trials are: tossing a coin three times rolling a pair of dice 10 times production on an assembly line These experiments share the following characteristics: they have exactly two outcomes: success OR failure each trial is independent the probability of each outeome is the same for each trial of the experiment Any experiment with these characteristics is called a Bernoulli trial (named after the Swiss mathematician Jacob Bernoulli. one of the first to work on probability). The calculation of probabilities in such experiments is closely linked to the binomial theorem. The binomial model applies to situations that are equivalent to drawing from a hat without replacement. The probabilities for various events determined by a Bermoulli experiment can be found easily by using the binomial expansion.

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