Choosing Distributions

A random variable that follows a Poisson distribution is a discrete random variable
A Poisson distribution is used when the random variable counts something
- The number of occurrences of an event in a given interval of time or space
There are three conditions that must fulfil to follow a Poisson distribution
- The mean number of occurrences is known and finite (λ)
- The events occur at random
- The events occur singly and independently

A random variable that follows a normal distribution is a continuous random variable
A normal distribution is used when the random variable measures something and the distribution is:
- Symmetrical
- Bell-shaped
A normal distribution can be used to model real-life data provided the histogram for this data is roughly symmetrical and bell-shaped
- If the variable is normally distributed then as more data is collected the outline of the histogram should get smoother and resemble a normal distribution curve

4-4-1-modelling-with-distributions-diagram-1

Knowledge of using the binomial and geometric distribution is expected for Statistics 2
Remember the three conditions for both distributions
- The trials are independent
- There are exactly two outcomes of each trial (success or failure)
- The probability of success(p) is constant
You will be expected to recognise when a random variable follows a binomial or geometric distribution and use their properties
- A binomial distribution will have a fixed finite number of trials(n)
- A geometric distribution will continue the trials until the first success

Always state what your variables and parameters represent. Make sure you know the conditions for when each distribution is (or is not) a suitable model.

Choosing Distributions (CIE A Level Maths: Probability & Statistics 2)