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adarshnor
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Hey guys, can you help me with the proofing of E(X) = r/p and Var(X) = rq/p^2
A negative binomial distribution is a probability distribution that represents the number of successes in a series of independent and identical trials before a specified number of failures occur. It is often used to model count data, such as the number of customers who make a purchase in a store or the number of accidents that occur in a factory in a given time period.
While both a negative binomial distribution and a binomial distribution involve counting the number of successes in a series of trials, the key difference is that a negative binomial distribution does not have a fixed number of trials. In a binomial distribution, the number of trials is predetermined, while in a negative binomial distribution, the number of trials continues until a specified number of failures occur.
The parameters of a negative binomial distribution are the probability of success in each trial (denoted by p) and the number of failures that must occur before the experiment is stopped (denoted by r). These parameters determine the shape and characteristics of the distribution.
The negative binomial distribution is similar to the Poisson distribution in that both are used to model count data. However, the Poisson distribution is used when the number of events in a fixed time or space is of interest, while the negative binomial distribution is used when the number of trials needed to achieve a certain number of successes is of interest.
The negative binomial distribution has many applications in fields such as business, economics, and engineering. Some examples include predicting the number of sales in a store, estimating the number of defective products in a manufacturing process, and determining the number of accidents in a given time period in a construction site.