Let X denote the number of customers entering the store in a given day and letYdenotethe number of female customers in that day. AssumeXhas a Poisson distribution with rateλ (pmf: λke−λ/k! for k= 0,1,2,...). Assume that given X, the distribution of Y is binomial with X trials and probability of success 1/2. (a) Give a reason why one might use the binomial as a model for Y given X.(b) ComputeE(Y) by relating it to the conditional mean of Y given X. (c) ComputeVar(Y). (d) Find the conditional distribution of X given Y.
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.
Let X denote the number of customers entering the store in a given day and letYdenotethe number of female customers in that day. AssumeXhas a Poisson distribution with rateλ (pmf: λke−λ/k! for k= 0,1,2,...). Assume that given X, the distribution of Y is binomial with X trials and probability of success 1/2.
(a) Give a reason why one might use the binomial as a model for Y given X.(b) ComputeE(Y) by relating it to the conditional mean of Y given X.
(c) ComputeVar(Y).
(d) Find the conditional distribution of X given Y.
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