Let X­­1 ~ Binomial(n1, p), and let X2 ~ Binomial(n2, p), independent of X1.  Show using a discrete transformation that Y = X1 + X2 ~ Binomial(n1 + n2, p).  Explain why this result makes sense intuitively.  Hint: the hypergeometric distribution may be helpful in finding the final marginal p.m.f.

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A: The graph is shown below:

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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.