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Math Help - Poisson approximation

  1. #1
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    Poisson approximation

    Question : If the probability that an individual suffers from a bad reaction from an injection of a given serum is 0.001, determine the probability that out of 2000 individuals
    i) exactly 3 individuals will suffer a bad reaction,
    ii) more that 2 individuals will suffer a bad reaction by using Poisson approximation. Also give exact probabilities( you need not simplify the expression)
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  2. #2
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    Quote Originally Posted by zorro View Post
    Question : If the probability that an individual suffers from a bad reaction from an injection of a given serum is 0.001, determine the probability that out of 2000 individuals
    i) exactly 3 individuals will suffer a bad reaction,
    ii) more that 2 individuals will suffer a bad reaction by using Poisson approximation. Also give exact probabilities( you need not simplify the expression)
    What have you tried? Where are you stuck? What thoughts do you have? Do you know what the Poisson approximation is an approximation to? Have you looked up the Poisson approximation in your classnotes or textbook?
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  3. #3
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    Please check if it is correct or no

    Quote Originally Posted by mr fantastic View Post
    What have you tried? Where are you stuck? What thoughts do you have? Do you know what the Poisson approximation is an approximation to? Have you looked up the Poisson approximation in your classnotes or textbook?
    i)
    p(x, \lambda) = \frac{\lambda^{-x}}{x!} . e^{- \lambda}

    \lambda = n \theta

    \lambda \ = \ 2

    p(3, \lambda)= \frac{e^{-2}}{3!} . 2^3 = \frac{4 e^{-2}}{3} ...............Is that correct ?

    ii) P(X>2, \lambda) = ___________............I dont know what to do ?



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  4. #4
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    For the second one, add up the probabilities for 0 to 2 and subtract from 1.

    The first one looks OK.
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