Choosing Distributions (Cambridge (CIE) A Level Maths): Revision Note

Choosing Distributions

When should I use a Poisson distribution?

• 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

When should I use a normal distribution?

• 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

Will I still be expected to use the binomial and geometric distribution

• 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