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The Binomial Distribution

幫考網校2020-08-07 09:36:50
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The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure). The distribution is characterized by two parameters: the probability of success in each trial (denoted by p) and the number of trials (denoted by n).

The probability of getting exactly k successes in n trials is given by the binomial probability formula:

P(k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) is the number of ways to choose k items from a set of n items, and is equal to n!/(k!(n-k)!).

The mean and variance of the binomial distribution are given by:

mean = np
variance = np(1-p)

The binomial distribution is widely used in statistics and probability theory to model a variety of phenomena, such as the number of heads in a series of coin flips, the number of defective items in a batch of products, and the number of successful sales calls in a marketing campaign.
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