Bernoulli Trials Two Possible Outcomes Trials are independent.

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Presentation transcript:

Bernoulli Trials Two Possible Outcomes Trials are independent. Success, with probability p Failure, with probability q = 1  p Trials are independent.

Binomial Distribution For n Bernoulli trials, the number of successes X is a binomial random variable. The probability of k successes is given by the binomial probability formula: As k varies with fixed n and p, the binomial probabilities define a binomial probability distribution over {0, 1, 2, …, n}.

Mean and Standard Deviation of a Binomial RV

Law of Large Numbers Informal: If n is large, the proportion of successes in n Bernoulli trials will be very close to p. Formal: For Bernoulli trials with n and p, as n  , for all  > 0, where k is the number of successes in the n trials.