Consider the following statements regarding Poisson Distribution:
(A) It is a continuous probability distribution. (B) It is applicable when 'n' the number of trials is indefinitely large and 'p' the probability of success is indefinitely small. (C) Its mean is equal to its variance.
Which of the above statements are correct?

Correct option is B

Explanation
· Statement (A) is incorrect because the Poisson distribution is a discrete probability distribution. It models the number of events occurring in a fixed interval of time or space, under the condition that these events happen independently of each other.
· Statement (B) is correct. The Poisson distribution can be derived as an approximation to the binomial distribution when the number of trials n is large, and the probability of success p is small, such that the product np (the expected number of successes) is a finite value.
· Statement (C) is also correct. In a Poisson distribution, the mean λ (lambda) is equal to its variance λ, which is a key characteristic of this distribution.
Information Booster
· Poisson Distribution: Typically used to model count data, such as the number of phone calls received by a call center in an hour.
· Key Properties: The Poisson distribution is characterized by its mean and variance being equal (λ).
· Applications: Commonly applied in fields such as telecommunication, traffic flow, and natural phenomena where events occur randomly.
· Relation to Binomial: When n is large and p is small, the binomial distribution B(n,p) approaches the Poisson distribution with λ=np.
Additional Information
· Example of Poisson Events: Occurrences of earthquakes in a region, arrivals of customers at a store, or failures of a machine part over a specified period.
· Mathematical Expression: The probability mass function of a Poisson random variable XXX is given by:

where k is the number of occurrences, λ is the average rate of occurrence, and e is the base of the natural logarithm.