bernoulli, binomial, hypergeometric

bernoulli, binomial, hypergeometric - Section 5.3: Binomial...

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Section 5.3: Binomial Random Variables Many problems in probability involve independently repeating a random experiment and observing at each repetition whether a specified event occurs. We label the occurrence of the specified event a success and the nonoccurrence of the specified event a failure . Bernoulli Trials: A success could be a female child, a head from a coin flip, a 5 on a die, a defective part, a black in roulette, etc. A success can take on a positive or negative connotation in the context of the example; it is merely the event we are interested in. Each repetition of the random experiment is called a trial, and collectively, all the trials are called Bernoulli Trials . We denote p as the probability of a success on 1 trial. p remains constant from trial to trial. Conditions for Bernoulli: 1) the trials are independent of one another 2) the result of each trial is classified as a success or failure, depending on whether or not a specified event occurs, respectively 3) the success probability and therefore the failure probability remains the same from trial to trial Note: If we sample from a population 1 at a time, it is Bernoulli if we sample with replacement but IT IS NOT BERNOULLI if we sample without replacement! Human Examples: Success= if the person is in school, if they have a college degree, if they have a job, if they have brown hair, etc. Sometimes the Bernoulli Distribution is called an indicator function, i.e. it lets one know whether or not a specific event has occurred.
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bernoulli, binomial, hypergeometric - Section 5.3: Binomial...

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