The Poisson Distribution (Edexcel A-Level Further Mathematics): Quizzes

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The Poisson Distribution
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What does the exponential distribution model, compared to the Poisson distribution?

Time between events

Which THREE conditions must events satisfy to be modelled by a Poisson distribution?

Rare, constant rate, independent

If the mean of an exponential distribution is 200, what is the value of λ\lambda?

1200\frac{1}{200}

If R∼Po(4)R \sim Po(4) and B∼Po(9)B \sim Po(9), what distribution does (R+B)(R + B) follow?

Po(13)Po(13)

For X∼Po(λ)X \sim Po(\lambda), how do you calculate P(X>4)P(X > 4)?

1−P(X≤4)1 - P(X \leq 4)

What type of values can the Poisson distribution take?

Integer values only

What is the probability mass function for X∼Po(λ)X \sim Po(\lambda)?

P(X=r)=e−λλrr!P(X=r)=\frac{e^{-\lambda}\lambda^r}{r!}

If events occur at rate 13 per hour, what is the rate per 8 hours for Poisson modelling?

104104

For R∼Po(4)R \sim Po(4) and B∼Po(9)B \sim Po(9), how do you find P(R=5 and B=6)P(R=5 \text{ and } B=6)?

P(R=5)×P(B=6)P(R=5) \times P(B=6)

Which type of distribution is the exponential distribution?

Continuous

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