Poisson & Binomial Distributions (Edexcel A-Level Further Mathematics): Quizzes

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Poisson Approximations of Binomials
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When can B(n,p)B(n,p) be approximated by Poisson distribution?

nn large, pp small, np≤10np \leq 10

For B(1000,0.002)B(1000, 0.002), what is λ\lambda for Poisson approximation?

λ=2\lambda = 2

Which scenario is suitable for Poisson approximation?

n=500n=500, p=0.01p=0.01, np=5np=5

For Y∼Po(λ)Y \sim \text{Po}(\lambda), what are the mean and variance?

Both equal λ\lambda

What is the Poisson probability formula?

P(Y=x)=λxe−λx!P(Y=x) = \frac{\lambda^x e^{-\lambda}}{x!}

Why use Poisson approximation for large nn and small pp?

Simplifies calculations

For Y∼Po(2)Y \sim \text{Po}(2), what is P(Y=2)P(Y=2)?

0.27060.2706

How does Poisson approximation compare to exact binomial?

Close but an estimate

What is a common mistake when using Poisson approximation?

Forgetting to calculate λ=np\lambda = np

What context commonly uses Poisson distribution?

Rare events over time or space

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