The random variable x is the number of occurrences of an event over an interval of ten minutes.It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length.It is known that the mean number of occurrences in ten minutes is 5.3.Which of the following discrete probability distributions' properties are satisfied by random variable x?

A) Normal
B) Poisson
C) Binomial
D) Hypergeometric

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Pembroke Brave · Accepted Answer

Final Answer : B, Explanation :  The Poisson distribution is the best choice because it models the number of occurrences of an event in a fixed interval of time, given a known rate of occurrence. In this case, the mean number of occurrences in ten minutes is 5.3, which gives us the rate parameter for the Poisson distribution. The other options are not appropriate because they assume different conditions, such as fixed sample size (binomial) or sampling without replacement (hypergeometric). The normal distribution might be a possibility if the sample size was very large, but we do not have that information here.

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