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Probability and Statistics

Quick questions on Binomial and Poisson distributions explained: H2 Mathematics Probability and Statistics

6short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are combining Poisson variables?
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If X∼Po(λ1)X \sim \mathrm{Po}(\lambda_1) and Y∼Po(λ2)Y \sim \mathrm{Po}(\lambda_2) are independent, then X+Y∼Po(λ1+λ2)X + Y \sim \mathrm{Po}(\lambda_1 + \lambda_2): rates over combined intervals add.
What is wrong variance?
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Binomial variance is np(1−p)np(1-p), Poisson variance is λ\lambda (equal to its mean).
What is mismatched interval for Poisson?
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Scale λ\lambda to the interval in the question (for 33 per minute over 55 minutes use λ=15\lambda = 15).
What is q1?
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State the mean and variance of B(50,0.2)\mathrm{B}(50, 0.2). [2 marks]
What is q2?
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For X∼Po(4)X \sim \mathrm{Po}(4), find P(X=0)\mathrm{P}(X = 0). [2 marks]
What is q3?
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State one condition distinguishing when to use the Poisson rather than the binomial. [1 mark]

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