Question

How to know which distrubiton formula to use, for example: Normal, Binomial, Negative Binomial, Geometric, Poisson, Exponential, Hyper geometric

I have a stats test tomorrow, and just need help when each is used or how to tell them apart.

Answer 1

For problems involving finding exact or numerical probabilities, chances are you will explicitly be given a particular distribution. However, some problems do in fact suggest that you know *which* distribution works best in a given scenario. Typically, you might want to first discern whether a given scenario is best described by a continuous versus a discrete distribution. This will tell you whether the most applicable distribution may be the normal versus the (negative) binomial, or the exponential versus the Poisson, for instance.

When you're given a certain event of interest \(E\) with a probability \(p\) of occurring, you may be asked to find the probability that \(E\) occurs a set number of times \(k\) within a set number of trials \(n\). You can view the occurrence of \(E\) as something along the lines of drawing a card from a deck \(\textit{with replacement}\). This essentially means that for any two or more times \(E\) is observed to occur, each occurrence is independent of another.

Where the binomial counts the actual number of successes occurring within a set number of trials, the negative binomial counts the number of trials needed to obtain a set number of successes.

The geometric distribution is actually a special case of the negative binomial. Geo is used to count the number of trials until the first occurrence of \(E\) (or perhaps until the first occurrence of something other than \(E\), depending on the context of the problem).

The hypergeometric distribution is much like the binomial distribution, but it's used with small populations, and you are counting the number of successes in a drawn sample \(\textit{without replacement}\).

The Poisson and exponential distributions are related, the difference being that one is discrete while the other is continuous. Poisson counts the number of times \(E\) occurs in a given time interval, whereas the exponential describes the wait time between occurrences of \(E\). In both cases, you would be given an average number of times that \(E\) might occur within a certain amount of time (a rate); for example, you might be given that within one hour, 20 cars pass through an intersection (20 cars per 1 hour).