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

Author

Amber

Expertise

Maths

## 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

#### Exam Tip

• 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.

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