Introduction to probability distributions — Edexcel A-Level Statistics
Test yourself on Introduction to probability distributions with PEARSON EDEXCEL A-Level practice questions.
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Introduction to probability distributions explained
Variability terms describe how values behave and how variables relate.
Read the full explanation
A random variable takes values determined by chance, such as the number shown when a fair die is rolled. A discrete variable takes countable values, often whole numbers, such as the number of goals in a match. A continuous variable can take any value in an interval, such as the mass of a parcel in kilograms. Two variables are independent when the value of one gives no information about the other, for example the outcomes of two separate fair coin tosses. They are dependent when knowing one changes the probability distribution of the other, for example the total rainfall and the number of umbrellas sold on a given day.
Your focus
- State the meaning of random, discrete, continuous, dependent and independent.
- Classify a given variable or pair of variables using the correct term.
- Select the option that applies the variability terms accurately to a context.
Introduction to probability distributions exam tips
Marking Points
- Defines a random variable as one whose value depends on the outcome of a chance experiment.
- Distinguishes discrete variables, which take countable values, from continuous variables, which take any value in an interval.
- Explains independence as the situation where the value of one variable does not affect the distribution of the other.
- Explains dependence as the situation where knowing the value of one variable changes the probability distribution of the other.
- Applies the correct term to a given context, for example classifying waiting time as continuous and count of defects as discrete.
Examiner Tips
- 💡Match each option to the definition before choosing, rather than relying on everyday meanings of the words.
- 💡For discrete versus continuous, ask whether intermediate values are meaningful, such as 2.5 goals versus 2.5 kilograms.
- 💡For dependent versus independent, ask whether knowing one value changes the probability of the other.
Common Mistakes
- Treating discrete as meaning small and continuous as meaning large: the distinction is about countable versus interval values, so the correction is to classify by the type of value, not its size.
- Assuming any two variables measured together are dependent: dependence requires a change in distribution, so the correction is to check whether one variable informs the other.
- Confusing random with unpredictable in a way that ignores probability: a random variable still has a defined probability distribution, so the correction is to describe that distribution.
- Calling a count continuous because it can grow large: counts remain discrete, so the correction is to check whether values are countable.