Professors Bennett and Sattler each independently pick k problems uniformly at random from a set of k2 problems to place on an exam. How many problems do we expect will be picked by both of them? How many problems do we expect will be picked by exactly one of them? The expected number of problems picked by both of them is: The expected number of problems picked by exactly one of them is:
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.
Professors Bennett and Sattler each independently pick k problems uniformly at random from a set of k2 problems to place on an exam. How many problems do we expect will be picked by both of them? How many problems do we expect will be picked by exactly one of them?
The expected number of problems picked by both of them is:
The expected number of problems picked by exactly one of them is:
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