Poisson Distributions

# POISSON DISTRIBUTIONS ASSIGNMENT HELP

Poisson Distributions

Important discrete probability distribution is Poisson exponential distribution, named after Simeon Demis Poisson, a Frenchmen who developed the distribution from studies in 1837. The Poisson distribution is used to describe a number of processes that involves an observation per unit of time or space. The binomial distribution is based on ascertaining the probability of a ‘r’ success in one trial. What then constitute one trial in a Poisson/Distribution? In the case of a batch of parts, an observation of a single part to determine whether it is defective is of a single part to determine whether it is defective, is of course, a trial.

#### Properties of Poisson distribution:

Like binomial distribution, the Poisson distribution has three significant attributes. They are mean, standard division and shape of the distribution.

• The mean of the Poisson distribution is equal to nP (μ). The value of ‘μ’ is usually a small positive number.
• The variance of Poisson distribution is also ‘μ’. The variance of binomial distribution is equal to npq of nP (1 – P). As P approaches O, the limit of the last factor (1 – P) approaches 1 and variance approaches nP or μ. The standard deviation of Poisson distribution is equal to √μ or √nP. From this we can draw a inference that Poisson distribution has only one parameter i.e. μ.

#### Shape of the Poisson distribution:

The Poisson distribution is positively skewed (P being small). Given the value of P, nP, will increase in n. As μ or nP increases, the Poisson distribution will be closer and closer to bell shaped distribution. That is why, normal distribution is also the limit of the Poisson distribution.

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