Discrete and Continuous Random Variables (AQA A-Level Further Maths): Quizzes

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The Poisson Distribution
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What is the unique property of the Poisson distribution regarding mean and variance?

Mean = Variance = λ\lambda

What does the acronym RICE represent for Poisson distribution conditions?

Random, Independent, Constant, Events

What does a Poisson distribution model?

Random events in fixed time/space intervals

In the notation X∼Po(λ)X \sim \text{Po}(\lambda), what does λ\lambda represent?

The mean rate of occurrence

If X∼Po(5)X \sim \text{Po}(5) and Y∼Po(8)Y \sim \text{Po}(8) are independent, what is X+YX + Y?

Po(13)\text{Po}(13)

Events occur at 3 per hour. What is λ\lambda for a 4-hour period?

1212

How can you test if observed data follows a Poisson distribution?

Check if sample mean ≈\approx sample variance

In the formula P(X=x)=e−λλxx!P(X = x) = \frac{e^{-\lambda} \lambda^x}{x!}, what is ee?

Mathematical constant ≈2.71828\approx 2.71828

Which scenario is appropriate for a Poisson distribution?

Cars on a quiet rural road (no queues)

If X∼Po(16)X \sim \text{Po}(16), what is the standard deviation of XX?

44

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Discrete and Continuous Random Variables

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Discrete and Continuous Random Variables

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Discrete and Continuous Random Variables

Hypothesis Testing and Contingency Tables

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Discrete and Continuous Random Variables

Hypothesis Testing and Contingency Tables

Random Processes

Hypothesis Testing and the t-Test

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