If someone tells us that a random variable is described by a Binomial or Poisson

Question

If someone tells us that a random variable is described by a Binomial or Poisson distribution, it becomes a very simple matter (presuming we know the key parameters) to be able to then predict the likelihood that any particular combination of values will be seen in a dataset containing that variable. Sometimes, though, we don't know what kind of distribution our variable will fit, or we don't know enough to be able to identify the key parameters needed to make accurate predictions Part of the analysis we routinely do with datasets is to identify whether or not any of the variables included are Binomial or Poisson in nature. Discuss why it can be helpful to do this? Discuss how you would identify which variables in the dataset would benefit from such analysis. Does it provide benefit to name the distribution that applies even if you can't precisely identify the needed parameters for that distribution? Use specific examples in your post: Provide some examples of variables that might be in your data that would be considered Binomial or Poisson. These examples should demonstrate that you understand how to recognize that a variable fits one of these distributions

Explanation / Answer

Any trial of experiment which results in two outcomes like True/false, Yes/No etc are called Bernoulli trial.

And If we perform such trial some fix number of time then the Distribution of a random variable on such trial is said to be Binomial distribution.

For example tossing a coin three time.

X: Getting number of heads. (## random variable)

here the parameter's are

n= 3 ## Sample size

p= 0.5 ## probability of success that is getting head.

If the rate of occuring the event is constant then the distribution is said to be a poisson distribution.

for example the accident occures at any given point in a day.

Number of phone calls received in a reception in an hour.

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