Cars cross a certain point on the highway in accordance with a poisson process with rate = 3 per minute. if al runs across the highway at some random time, what is the probability that he will avoid being hit by a car if the amount of time that it takes him to cross the road is 10 seconds? hint: assume that if a car goes by while al is on the highway, that it will hit him.

The probability is 0.2212

Solution:

As per the question:

Poisson rate,

Now,

Let

X: time of waiting for the next vehicle on the highway

Now,

To find the probability of the next vehicle to arrive after 10 s

The probability distribution function is given by:

Now,

P(X < x) =

For X> 0,

P(X > x) =

P(X < 5) =

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