STAT 35000 Lecture Notes - Lecture 3: Binomial Distribution, Random Variable, Standard Deviation

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Binary there are only two possible outcomes for each trial. Independent the outcome of trials are independent. N- n indential trials where n is fixed. S success: for each trial, the probability of success must be the same: notation: Than two outcomes: the probability of getting a full house poker hand, example problem: After the festive night of the fourth of july, the police arrested a large number of people accused of drunken driving. Out of a group of 40 arrested men 85% of them are first time offenders. Is the given distribution a binomial distribution: what is the probability that 6 of these 40 men are repeat offenders, find the mean and standard deviation of the given distribution, the given distribution is a binomial distribution because: B there are only two possible outcomes: repeated offenders, first time offenders. I each of the outcomes are independent of each other. N the number of trials is fixed (40)