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 cant precisely identify the needed parameters for that distribution? Post your response of 1-3 paragraphs (about 100-200 words) by the due date for this discussion assignment, and then reply to at least two initial responses of your peers during the remainder of the week, particularly focusing on responses that might differ from your own. Also respond appropriately to anyone who posts questions against your own postings. Discuss the content! Keep responses focused on the substance of the issue, not simply on agreeing with a comment or encouraging each other.
Explanation / Answer
As weall know that poisson variable takes values from zero to positive infinity and it is modelled for rare events where as for binomial random variable the domain is finite and it is 0,1,...n. in posson domain is infinite and binomial domain is finite.for poisson expectation and variance are equal where as for binomial expectation is ;arge than the variance.poisson is a one parameter family whereas binomial is a two parameter random variable.using these facts we can identify
again for binomial randpm variable=s we can categorise each trial as success and failure but in case of poisson random variable it generally explains rare events as poisson distribution is positively skewed.
