The correct answer is Poisson Distribution.

Probability distribution :

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• Probability distribution yields the possible outcomes for any random event.
• It is also defined based on the underlying sample space as a set of possible outcomes of any random experiment.
• These settings could be a set of real numbers or a set of vectors or a set of any entities.

Key Points

Poisson distribution :

• The Poisson distribution is a discrete probability function that means the variable can only take specific values in a given list of numbers, probably infinite.
• A Poisson distribution measures how many times an event is likely to occur within an “x” period of time.
• In other words, we can define it as the probability distribution that results from the Poisson experiment.
• A Poisson experiment is a statistical experiment that classifies the experiment into two categories, such as success or failure.
• Poisson distribution is a limiting process of binomial distribution.

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Important Points The formula for the Poisson distribution function is given by:

f(x) =(e- λ λx)/x!

Where,

• e is the base of the logarithm
• x is a Poisson random variable
• λ is an average rate of value

Thus, in Poisson distribution, the mean value of the distribution (λ) is the sole parameter of the distribution.

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Additional Information Binomial distribution:

• The binomial distribution is a probability distribution in statistics that summarizes the likelihood that a value will take one of two independent values under a given set of parameters or assumptions.
• The underlying assumptions of the binomial distribution are that there is only one outcome for each trial, that each trial has the same probability of success, and that each trial is mutually exclusive or independent of one other.

Normal Distribution:

• Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
• In graphical form, the normal distribution appears as a “bell curve“.

Exponential distribution:

• The exponential distribution is a continuous probability distribution that often concerns the amount of time until some specific event happens.
• It is a process in which events happen continuously and independently at a constant average rate.

Hence, in Poisson distribution, the mean value of the distribution (λ) is the sole parameter of the distribution.

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