CIE A Level Maths: Probability & Statistics 2复习笔记2.4.1 Choosing Distributions
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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