1. Suppose that the number of cars passing a certain point of some road per minute between 8am and 10am on a Sunday morning follows a Poisson distribution with mean λ = 5. A traffic inspector has arrived at the specified location during the aforementioned period. She notes the wait time W1 for the next car to pass by the location. (a) What distribution does W1 follow? What are its expectation and variance? (b) What is the probability she needs to wait more than 1 minute before the next car passes by? (c) What is the probability that she needs to wait more than 1 minute for 2 cars to pass by?
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.
1. Suppose that the number of cars passing a certain point of some road per minute between 8am and 10am on a Sunday morning follows a Poisson distribution with mean λ = 5. A traffic inspector has arrived at the specified location during the aforementioned period. She notes the wait time W1 for the next car to pass by the location.
(a) What distribution does W1 follow? What are its expectation and variance?
(b) What is the probability she needs to wait more than 1 minute before the next car passes by?
(c) What is the probability that she needs to wait more than 1 minute for 2 cars to pass by?
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