A parking lot has two entrances. Cars arrive at entrance I according to a Poisson distribution at an average of 3 per hour and at entrance II according to a Poisson distribution at an average of 2 per hour. What is the probability that a total of 3 cars will arrive at the parking lot in a given hour? What is the probability that less than 3 cars will arrive at the parking lot in a given hour? (Assume that the numbers of cars arriving at the two entrances are independent. (Note: The probability mass function of Poisson distribution is p(x) = (e^-λ * λ^x)/(x!) for x = 0,1,2, ..., , where λ is the parameter which indicates the average number of events in the given time interval.)

(a) the probability that a total of 3 cars will arrive at the parking lot in a given hour is 0.1404.

(b) The probability that less than 3 cars will arrive at the parking lot in a given hour is 0.1247.

Step-by-step explanation:

Let X = cars arriving through entrance I and Y = cars arriving through entrance II.

Given:

The probability function of a Poisson distribution is:

It is also provided that the events X and Y are independent.

Let U = X + Y

Then E (U) = E (X) + E(Y) = 3 + 2 = 5.

The random variable U also follows a Poisson distribution with parameter λ = 5

(a)

The probability that a total of 3 cars will arrive at the parking lot in a given hour is:

Thus, the probability that a total of 3 cars will arrive at the parking lot in a given hour is 0.1404.

(b)

The probability that less than 3 cars will arrive at the parking lot in a given hour is:

Thus, the probability that less than 3 cars will arrive at the parking lot in a given hour is 0.1247.

black/brown

step-by-step explanation:

well, you see here, jamal was born to 2 parents, his mother who he lives with and his father who left at a young age and who happens to be younger than him. he stole cookies because he has to steal food due to the fact that he spends his government poverty checks on pot and women.

answer: 48

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