Poisson distribution may bea)unimodal.b)bimodal.c)Multi-modal.d)(a) or...
The Poisson distribution has a single parameter, λ . For a Poisson distribution modeling a binomial phenomenon, λ can be taken as an approximation of np.In such a case, a Poisson distribution with the appropriate parameter λ will approximate the distribution of events over time or the number of events in an interval.is unimodal.and multi-modal..
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Poisson distribution may bea)unimodal.b)bimodal.c)Multi-modal.d)(a) or...
Explanation:
Poisson distribution is a probability distribution that is used to describe the occurrence of rare events in a fixed interval of time or space. It has the following properties:
- It is a discrete distribution, which means that it is defined only for integer values.
- It is unimodal, which means that it has only one peak.
- Its mean and variance are equal.
- Its shape depends on the parameter λ, which is the expected number of occurrences in the interval.
However, in some cases, the Poisson distribution may exhibit some deviations from its typical shape, which could make it look bimodal or multi-modal. These deviations could be caused by the following factors:
- Overdispersion: This occurs when the variance of the distribution is greater than its mean. In this case, the distribution may look wider than usual, and may have two or more peaks.
- Mixture distribution: This occurs when the data comes from two or more subpopulations that have different underlying Poisson parameters. In this case, the distribution may have two or more distinct peaks.
Therefore, the correct answer to the question is (a) or (b), depending on the specific characteristics of the data. If the data follows a typical Poisson distribution, then it is unimodal. However, if the data exhibits some deviations from the typical shape, then it could be bimodal or multi-modal.
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