1 point) Cars arrive at a \"Y\" in a road and must choose either the left fork o

Question

1 point) Cars arrive at a "Y" in a road and must choose either the left fork or the right fork. Assume that the number of cars that arrive at the fork has a Poisson distribution, and that the average number of cars that arrive at the "Y" per minute is 3. A car arriving at the fork chooses the left fork with probability 1/3 and the right fork with probability 2/3. What is the exact formula for the Poisson distribution that gives the number of cars that travel down the right fork per minute? Your answer should be a function of k and should have an exponent of "e" Warning: to type a factorial like k! in this problem, you need to type "fact(k).

Explanation / Answer

There are 3 cars arrive at fork per minute and probability that a car takes right fork is 2/3.

Hence expected number of cars that take right fork per minute is 3*2/3 = 2

= 2

Poisson's Distribution Formula:
P(X = x) = (e^-) (^x) / x!

P(X = k) = e^-2 * (2^k)/fact(k)

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