. Consider f(x, y) = x2 + 4xy + y? subject to the constraint r² + y² < 49 (a) Find all critical points of the function that lie in the interior of the disk and use the second derivative test to classify those points. (b) Using Lagrange multipliers, determine the complete system of equations to find the points on the boundary. (c) Solve the system and provide the point(s) on the boundary where f is optimized. Make sure you consider the case when x = 0 and when y = 0. (d) Which of those points maximizes f? (e) Which of those points minimizes f?

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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.