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Volume I
"Greedy"
Is Not Always "Safe"
By: Eric P. Kamprath
Abstract: We derive a formula for the probability of obtaining a specific object of given quality in a random permutation of unique objects. We propose strategies for maximizing the probability of obtaining the object of highest quality and for maximizing the expected value of the of the object obtained.
When To Expect A Catastrophe
By: Kathryn Nyman
Abstract: Given a sequence of independent trials, each
of which results in a failure with probability p, we find a recurrence
relation and a closed for for the expected number of trials until two
consecutive failures occur. Additionally, a recurrence relation is found
for the probability of n failures occurring for the first time
consecutively after k trials.
Are
Seven Game Baseball Series Still Fairer when Morale is Considered?
By: Scott Reske
Abstract: E. Lee May Jr. concluded in his article "Are Seven-Game Baseball Playoffs Fairer?" [1] that there is very little difference in fairness between a five and a seven game baseball series, roughly 3.7%. We address May's question concerning fairness when morale is included, concluding that if morale's affect is non-cumulative, then morale plays little to no difference in fairness between the five and seven game series.
The
Secret Santa Problem
By: Mike Reske
Abstract: Given a randomly generated directed path on a graph on n vertices that reaches every vertex once and only once, we find a recurrence relation for the expected value of the number of cycles.
Birthdays,
Birthdays, and More Birthdays
By: Brian Nach
Abstract: Considering generalizations of the well known birthday problem, we obtain the probability that n randomly chosen items from a set S include at least one pair of the same type and we also obtain the expected number of elements that must be chosen from S in order to obtain an element of a given type.
Will
A System Operate?
By: Cindy Yerges
Abstract: A system of n objects are lined in a row. There are m defective objects in this system. The system will be operable if no more than k defective objects are adjacent in this line. Using restricted equations and inclusion-exclusion, we will compute the probability that a randomly selected system of n objects with m defective objects will be operable.
What
Color Were Those Eyes?
By: Jennifer Jungknect
Abstract: We show that by examining the percentage of people with blue eyes in a population, we can further determine the percentage of people who have brown eyes as a result of a dominant-dominant genotype and the percentage of people with brown eyes as a result of a dominant-recessive genotype. This finding is based on the Hardy-Weinberg theorem.
The
World Is Seldom Ideal
By: Leon Siklossy
Abstract: Based on the Hardy-Weinberg Equation, we derive a recurrence relation for the probability of the extinction of the recessive gene in a population after m generations given a random radial deviation of q from the ideal in any one generation.
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