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Browse Classroom Capsules and Notes

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Displaying 41 - 50 of 70

Probabilities of Clumps in a Binary Sequence

A collection of cards, \(r\) with red faces \(b\) with black faces, are randomly laid face down in a row. What is the probability that \(t\) cards of the same color lie consecutively?

Majorization and the Birthday Inequality

It is known that the probability that at least two persons in a group have the same birthday, when the birthday distribution is not uniform, is no less than the probability when the...

Buffon's Needle Problem on Radial Lines

The author computes the probability of a variation of Buffon's needle problem with uniform angular spacing.

Whiskey, Marbles, and Potholes

A natural generalization of probability trees and hypergeomeric distributions is used to solve problems anti-intuitive to some.

Copulas, Characterization, Correlation, and Counterexamples

Copulas can be employed in probability and mathematical statistics courses.

Unexpected Occurrences of the Number \(e\)

The authors describe the Hat Check and several other problems leading naturally to the number \(e\).

Dropping Scores

Dropping the smallest or largest in a finite set of numbers does not necessarily lower the variance.

Computing the Fundamental Matrix for a Reducible Markov Chain

A Markov chain with 9 states is used to illustrate a technique for finding the fundamental matrix.

Child's Play
The author shows a clever block stacking process for counting the total number of ways each possible sum can be rolled using three standard dice.
Almost-Binomial Random Variables

The author discusses binomial distribution where \(n\) is replaced by any positive number.

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