Take a random permutation of the integers 1, 2, . . . , n. Let us say that the integers i and j with i ≠ j are switched if the integer i occupies the jth position in the random permutation and the integer j the ith position. What is the expected value of the total number of switches
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.
Take a random permutation of the integers 1, 2, . . . , n. Let us say that the integers i and j with i ≠ j are switched if the integer i occupies the jth position in the random permutation and the integer j the ith position. What is the
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