Question

The binomial and Poisson distributions are two different discrete probability distributions. Explain the differences between the distributions and provide an example of how they could be used in your industry or field of study.

Answer 1

Binomial distribution is used in the following situation:

1. The experiment has only two possible distinct outcomes, one is labelled 'succes' and other as 'failure'.

2. The experiment is repeated n times and the outcome of each one trial is independent of the other.

3. The probability of success remains constant at every repetition of the experiment. It is denoted by p.

The random variable is

X: The number of successes in n trials

The pdf is given by

Field example: A rocket containing, say 50 satellites is launched, probability that a satellite is launched successfully is 0.89 and the number of successfully launched satellites is the variable of interest.

Poisson distribution is used in the following case

When we are interested in the number of occurrences of some rare event in a short duration of time and a specified region.

Field exapmle:

X: Number of defectives produced in a lot of, say 1000 items produced in an factory.

Thus Binomial distribution has a finite sample space {0,1,..., n} whereas Poisson distribution has a countable sample space, which is {0,1,2,...}

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