. Suppose that the number of Bigfoot sightings per year in the Northwestern US is well-modeled by a Poisson random variable with an average

Question

. Suppose that the number of Bigfoot sightings per year in the Northwestern US is well-modeled by a Poisson random variable with an average of 3 sightings occurring per year. Calculate the probability that in a given year there are at least 4 sightings in this region, given that there are at least 2 sightings.

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Julia 5 days 2021-11-21T23:54:40+00:00 1 Answer 0

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    2021-11-21T23:56:27+00:00

    Answer:

    0.1944

    Step-by-step explanation:

    Given that  the number of Bigfoot sightings per year in the Northwestern US (say X) is well-modeled by a Poisson random variable with an average of 3 sightings occurring per year.

    P(X=x) = \frac{e^{-3} *3^x}{x!}\\\

    the probability that in a given year there are at least 4 sightings in this region, given that there are at least 2 sightings

    =Prob that there are atleast 4 sightings/Prob atleast 2 sightings

    (since intersection of these two events is atleast 4)

    =\frac{P(X\geq 4 }{P(X\geq 2} \\\\=\frac{0.184737}{0.950213} =0.194416

    Reqd prob = 0.1944

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