MATH SOLVE

4 months ago

Q:
# . 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.

Accepted Solution

A:

Answer:0.1944Step-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.[tex]P(X=x) = \frac{e^{-3} *3^x}{x!}\\\[/tex]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)=[tex]\frac{P(X\geq 4 }{P(X\geq 2} \\\\=\frac{0.184737}{0.950213} =0.194416[/tex]Reqd prob = 0.1944