The number of people that enter a drugstore in a given hour is a Poisson random variable with parameter λ = 10. Let M and W represent the number of men and women, respectively, that enter the store in a given hour. (Assume that each new customer is equally likely to be a man or a woman.) (a) Find the joint probability mass function of M and W. That is, find a formula for p(i, j) = P(M = i, W = j). (Hint: First write p(i, j) = P(M = i, W = j) = P(M = i, M + W = i + j) and then compute the term on the right-hand side by using the conditional probability formula P(A ∩ B) = P(A|B)P(B).) (b) Compute the conditional probability that at most 3 men entered the drugstore, given that 10 women entered in that hour.
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.
The number of people that enter a drugstore in a given hour is a Poisson random variable with parameter λ = 10. Let M and W represent the number of men and women, respectively, that enter the store in a given hour. (Assume that each new customer is equally likely to be a man or a woman.) (a) Find the joint
(b) Compute the conditional probability that at most 3 men entered the drugstore, given that 10 women entered in that hour.
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