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Full-Text Articles in Probability
Influences Of Probability Instruction On Undergraduates' Understanding Of Counting Processes, Kayla Blyman
Influences Of Probability Instruction On Undergraduates' Understanding Of Counting Processes, Kayla Blyman
Theses and Dissertations--Education Sciences
Historically, students in an introductory finite mathematics course at a major university in the mid-south have struggled the most with the counting and probability unit, leading instructors to question if there was a better way to help students master the material. The purpose of this study was to begin to understand connections that undergraduate finite mathematics students are making between counting and probability. By examining student performance in counting and probability, this study provides insights that inform future instruction in courses that include counting and probability. Consequently, this study lays the groundwork for future inquiries in the field of undergraduate …
Cycle Lengths Of Θ-Biased Random Permutations, Tongjia Shi
Cycle Lengths Of Θ-Biased Random Permutations, Tongjia Shi
HMC Senior Theses
Consider a probability distribution on the permutations of n elements. If the probability of each permutation is proportional to θK, where K is the number of cycles in the permutation, then we say that the distribution generates a θ-biased random permutation. A random permutation is a special θ-biased random permutation with θ = 1. The mth moment of the rth longest cycle of a random permutation is Θ(nm), regardless of r and θ. The joint moments are derived, and it is shown that the longest cycles of a permutation can either be positively or …