Problem 3

A person prepares to cross the street mid-block (ie, albeit at a signalized intersection or zebra crossing). To cross the street requires "s" seconds. Traffic on the street follows a Poisson process at rate ? (cars per second).

a.- Suppose the person does not look when crossing. Find the probability that she can cross without being hit by a car.

b.- Suppose now that the person will cross the street after the third car passes. How long will it take to cross the street? Consider that you are currently in time

? = 0.

c.-What is the probability that the time elapsed between two consecutive cars is less than ? minutes?

d.- The probability that between two successive arrivals is greater than 10 seconds.

m3 A person prepares to cross the street midblock (1g, albeit at a signalized intersection or zebra crossing). To cross the street requires "s" seconds. Traffic on the street follows a Poisson process at rate it (cars per second). a. Suppose the person does not look when crossing. Find the probability that she can cross without being hit by a car. b. Suppose now that the person will cross the street after the third car passes. How long will it take to cross the street? Consider that you are currently in time i=0. c.What is the probability that the time elapsed between two consecutive cars is less than 1\" minutes? d. The probability that between two successive arrivals is mm 10 gm