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Math Help - Poisson Problem

  1. #1
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    Poisson Problem

    If a random variable X follows Poisson distribution such that
    P(X=1) = P(X=2)
    Compute
    i) the mean of the distribution
    ii) P(X=0)
    iii) standard deviation of the distribution
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  2. #2
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    Hi

    Poisson distribution with parameter \lambda is such as
    P(X=k) = e^{-\lambda} \frac{\lambda^k}{k!}

    P(X=1) = e^{-\lambda} \lambda

    P(X=2) = e^{-\lambda} \frac{\lambda^2}{2}

    Therefore

    e^{-\lambda} \lambda = e^{-\lambda} \frac{\lambda^2}{2}

    which allows to compute the value of \lambda
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  3. #3
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    How this

    Quote Originally Posted by running-gag View Post
    Hi

    Poisson distribution with parameter \lambda is such as
    P(X=k) = e^{-\lambda} \frac{\lambda^k}{k!}

    P(X=1) = e^{-\lambda} \lambda

    P(X=2) = e^{-\lambda} \frac{\lambda^2}{2}

    Therefore

    e^{-\lambda} \lambda = e^{-\lambda} \frac{\lambda^2}{2}

    which allows to compute the value of \lambda
    --------------------------------------------------------------------

    I am getting \lambda=2 is this right
    And
    i) mean of distribution is \mu=2
    since \mu = \lambda

    ii)  P(X=0) = \frac{2^0 \ e^{-2}}{0!}
    =0.135

    iii) \sigma^2 = \mu
    ie \sigma^2 = 2
    Standard deviation = \sqrt{2}
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  4. #4
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    I agree with your answers !
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