Distributions - Edexcel A Level Further Maths

Binomial:
1) there are a fixed number of trials, n.
2) there are two possible outcomes (success and failure).
i.e. P(Success) = p and P(Failure) = 1 – p.
3) there is a fixed probability of success, p.
4) the trials are independent of each other.

So this will be when you have an integer number of trials, and you want to know the probability of a certain number/greater than/less than a certain number of them being successes.

Normal:
This is similar to the binomial, but is continuous (so heights, weights, battery life etc.). If your data is relatively symmetrical and bell shaped, then this is probably the one you're looking for.

Poisson:
Another continuous one, used to model the number of times that a particular event occurs within a given interval of time or space (e.g. number of chocolate chips in a cookie, number of patients arriving at a hospital each half hour etc.). Look out for anything mentioning average rate to spot this one!
For the Poisson distribution to be a good model, the events must occur:
1) independently
2) singly, in space or time
3) at a constant average rate so that the mean number in an interval is proportional to the length of the interval

This one is based on our parameter lambda, which is the mean number mentioned above. For a Poisson distribution to be a good model, the mean and variance will both be (roughly) equal to lambda.

Geometric:
If you are carrying out successive, independent trials, each with the same probability of success, you can model the number of trials needed to achieve a single success using the geometric distribution (e.g. how many times you need to roll a die until you get a six).

Negative binomial:
The binomial is used to model the number of successes in a fixed number of trials. The negative binomial models the number of trials needed to achieve a fixed number of successes (e.g. the chance you need 10 rolls of a die to get 3 sixes).