During rush hour, from 8 am to 9 am, traffic accidents occur according to a Poisson...

During rush hour, from 8 am to 9 am, traffic accidents occur according to a Poisson process with a rate of 5 accidents per hour. Between 9 am and 11 am, they occur as an independent Poisson process with a rate of 3 accidents per hour. What is the PMF of the total number of accidents between 8 am and 11 am?

Solutions

Expert Solution

Let X be the random variable that denotes the number of traffic accidents occurring between 8 am and 9 am.

X Poisson (₁ = 5)

Let Y be the random variable that denotes the number of traffic accidents occurring between 9 am and 11 am.

Y Poisson (₂ = 3)

X and Y are independent poisson random variables.

By the addition of independent poisson processes, let Z = X + Y

So, Z Poisson ( = ₁ + ₂)

Z Poisson ( = 5 + 3 = 8)

The pmf of the total number of accidents between 8 am and 11 am is

P(Z = z) = (e^-8 * 8^z) / z! ; z = 0, 1, 2, ...........

= 0 ; otherwise

orchestra answered 1 year ago

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