3.2.2 Example B Consider the three functions fi (k) = 3*, f2(k) = k3*, f3 (k) = k23k. (3.42) The linear combinations of these three functions can be written as follows: cifi(k)+ c2f2(k) + c3f3(k) = 3*(c1 + c2k + c3k?). (3.43) Note that the right-hand side of equation (3.43) will be zero if and only if C1 + c2k + c3k2 = 0. (3.44) %3D But this can only occur for cı = c2 = c3 = 0. Therefore, the three functions given in equation (3.42) are linearly independent. An easy calculation shows that the Casoratian for these functions is C(k) = 2 - 33k+3. (3.45) Since C(k) 0, we again conclude that these three functions are linearly independent.

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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.