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Math Help - Poisson Probabilities

  1. #1
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    Poisson Probabilities

    I have the following questions.

    The number of episodes per year of obtaining a certain disease follows poisson distribution has \mu = 1.6

    Find the probability of 3 or more episodes occuring over 2 years.

    I have \mu = 1.6\times 2 = 3.2

    \displaystyle P(X\geq 3) = 1- (P(X=0)+P(X=1)+P(X=2) )


    = 1-\left(\frac{e^{3.2}\times 3.2^0}{0!}+\dots \right) = 0.62

    Happy with that.

    Find the probability of not getting any episodes of the disease in a certain year

    so \displaystyle P(X=0) = \frac{e^{3.2}\times 3.2^0}{0!}= 0.201897

    Also happy with that.

    What is the probability that 2 siblings will both have 3 or more episodes in the first to years?

    Is this binomial given p = 0.62 finding P(X=2)? but what would n be?

    Or is it still poisson? maybe a different \mu = 0.62


    Thx!
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  2. #2
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    Re: Poisson Probabilities

    Quote Originally Posted by Bushy View Post
    I have the following questions.

    The number of episodes per year of obtaining a certain disease follows poisson distribution has \mu = 1.6

    Find the probability of 3 or more episodes occuring over 2 years.

    I have \mu = 1.6\times 2 = 3.2 .

    \displaystyle P(X\geq 3) = 1- (P(X=0)+P(X=1)+P(X=2) )


    = 1-\left(\frac{e^{3.2}\times 3.2^0}{0!}+\dots \right) = 0.62

    Happy with that.

    Find the probability of not getting any episodes of the disease in a certain year

    so \displaystyle P(X=0) = \frac{e^{3.2}\times 3.2^0}{0!}= 0.201897

    Also happy with that.

    What is the probability that 2 siblings will both have 3 or more episodes in the first to years?

    Is this binomial given p = 0.62 finding P(X=2)? but what would n be?

    Or is it still poisson? maybe a different \mu = 0.62


    Thx!
    Calculate p = \Pr(X \geq 3)

    Let Y be the random variable 'Number of children that have an episode in the first two years'.

    Then Y ~ Binomial(p = from above, n = 2).

    Calculate Pr(Y = 2). The answer will be p^2 = ....
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