A traffic light is red for 20 seconds and green for 40 seconds. Cars arrive at the traffic light as a Poisson process with rate 2 per minute. They take exactly 20 seconds to go through the light. A car cannot start going through until the previous one has cleared the light. Assuming, as an initial condition, that there are no cars at the traffic light when it turns red: a. What is the probability that at least one car will arrive when the light is still red? b. What is the probability that there will be no cars at the light when the light next turns red?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
A traffic light is red for 20 seconds and green for 40 seconds. Cars arrive at the traffic light as a Poisson process with rate 2 per minute. They take exactly 20 seconds to go through the light. A car cannot start going through until the previous one has cleared the light. Assuming, as an initial condition, that there are no cars at the traffic light when it turns red:
a. What is the
b. What is the probability that there will be no cars at the light when the light next turns red?
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