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Section 2.4, 3.1 Definitions MATH 166:503 February 24, 2015 Def: a Bernoulli trial is an experiment in which there are just two outcomes. Successive Bernoulli trials, called repeated Bernoulli trials, are assumed to be independent of each other. In repeated Bernoulli trials, one outcome is called a success and the other is called a failure. If p is the probability of success and q = 1 − p is the probability of failure, the probability of obtaining exactly k successes in n trials is C(n, k)pk q n−k . Remember: this computation requires that the trials are independent. Def: a random variable is a rule that assigns a real number to each outcome of an experiment. Def: a random variable is - finite discrete if it takes only finitely many values. - infinite discrete if it takes infinitely many values that can be listed. - continuous if it takes infinitely many values that cannot be listed. The area of the region of a histogram associated with a random variable X is P (X). P (n1 ≤ X ≤ n2 ) is the sum of the areas of the histogram from n1 to n2 . Def: the binomial distribution is the probability distribution for repeated Bernoulli trials. 1