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    Which of the following statements correctly describes the Poisson distribution?
    Question

    Which of the following statements correctly describes the Poisson distribution?

    A.

    It is used to model the number of successes in a fixed number of trials, each with the same probability of success

    B.

    It is symmetric and bell-shaped, suitable for continuous data

    C.

    It models the number of events occurring in a fixed interval of time or space when these events happen with a known constant mean rate and independently of the time since the last event

    D.

    It assumes that all outcomes are equally likely over a given interval

    Correct option is C

    The Poisson distribution is a discrete probability distribution that models the number of occurrences of an event in a fixed interval of time or space, given that:

    • Events occur independently.

    • The mean rate (λ) of occurrence is constant.

    • Two events cannot occur simultaneously.

    This distribution is especially useful in modeling rare events such as the number of phone calls at a call center in one hour, or the number of decay events from a radioactive source per second.

    Information Booster:

    1. Poisson distribution is characterized by a single parameter, λ (lambda), which is both the mean and variance of the distribution.

    2. It is used widely in queueing theory, reliability engineering, inventory management, and service operations.

    3. Its probability mass function is:

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