Statistics and Probability Commons^™

Teaching Introductory Statistics: A Graphical Relationship Between The Cumulative Distribution Function And The Probability Distribution Function, Dwight Adamnson, Scott Fausti

Economics Staff Paper Series (1969 - 2017)

Introductory statistics textbooks typically develop the concept of continuous random variables with a discussion of only the variables' probability distribution function and omit any discussion of the cumulative distribution function. The cumulative distribution function, however, is useful in developing the concepts of a normal distribution, the standard normal distribution and the probability of a continuous random variable falls within a specific range of values since the standard normal statistical table is derived from the cumulative distribution function. This paper develops a simple graphical relationship between a continuous random variables' cumulative distribution function and its probability distribution function that can be …

Optimization In Chemical Kinetics, Arthur T. Benjamin, Gordon J. Hogenson '92

All HMC Faculty Publications and Research

No abstract provided in this article.

Reply To Valverde, Paul B. Thompson

RISK: Health, Safety & Environment (1990-2002)

Professor Thompson responds to Valverde's argument, in the last issue, that his approach to Risk puts too much emphasis on the distinction between Risk subjectivism and Risk objectivism. In doing so, he asserts, inter alia, that anchoring Risk judgments in a probabilistic framework does not go far enough in rejecting reigning Risk-analysis notions of "real Risk."

The Cognitive Status Of Risk: A Response To Thompson, L. James Valverde

RISK: Health, Safety & Environment (1990-2002)

Discussing the role that probability theory should play in Risk analysis and management, Dr. Valverde argues that Thompson's approach puts too much emphasis on the distinction between Risk subjectivism and Risk objectivism in addressing the question, "When are Risks real?"

Predictive Probabilities In Employee Drug-Testing, John M. Gleason, Darold T. Barnum

RISK: Health, Safety & Environment (1990-2002)

Substance abuse in the U.S. has been estimated to cost $99 billion annually through lower productivity. Yet the authors urge caution in attempting to reduce these costs and health and safety Risks. In doing so, they cite commonly high frequencies of false negatives and false positives in employee drug tests - the latter having the potential to do great injustice to many drug-free employees.

Notions Of Relative Ubiquity For Invariant Sets Of Relational Structures, Paul Bankston, Wim Ruitenburg

Mathematics, Statistics and Computer Science Faculty Research and Publications

Given a finite lexicon L of relational symbols and equality, one may view the collection of all L-structures on the set of natural numbers w as a space in several different ways. We consider it as: (i) the space of outcomes of certain infinite two-person games; (ii) a compact metric space; and (iii) a probability measure space. For each of these viewpoints, we can give a notion of relative ubiquity, or largeness, for invariant sets of structures on w. For example, in every sense of relative ubiquity considered here, the set of dense linear orderings on w is …

Risk Objectivism And Risk Subjectivism: When Are Risks Real, Paul B. Thompson

RISK: Health, Safety & Environment (1990-2002)

Typically, those who discuss Risk management envision a two-step process wherein, first, Risk is more or less objectively appraised and, second, the acceptability of those Risks is subjectively evaluated. This paper questions the philosophical foundations of that approach.

Probability Of Discrete Failures, Weibull Distribution, Mary Jo Hansen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The intent of this research and these is to describe the development of a series of charts and tables that provide the individual and cumulative probabilities of failure applying to the Weibull statistical distribution. The mathematical relationships are developed and the computer programs are described for deterministic and Monte Carlo models that compute and verify the results. Charts and tables reflecting the probabilities of failure for a selected set of parameters of the Weibull distribution functions are provided.

Reliable Computation In The Presence Of Noise, Nicholas Pippenger

All HMC Faculty Publications and Research

This talk concerns computation by systems whose components exhibit noise (that is, errors committed at random according to certain probabilistic laws). If we aspire to construct a theory of computation in the presence of noise, we must possess at the outset a satisfactory theory of computation in the absence of noise.

A theory that has received considerable attention in this context is that of the computation of Boolean functions by networks (with perhaps the strongest competition coming from the theory of cellular automata; see [G] and [GR]). The theory of computation by networks associates with any two sets Q and …

A Comparative Analysis Of The Use Of A Markov Chain Versus A Binomial Probability Model In Estimating The Probability Of Consecutive Rainless Days, Jack Wilfred Homeyer

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Markov chain process for predicting the occurence of a sequence of rainless days, a standard technique, is critically examined in light of the basic underlying assumptions that must be made each time it is used. This is then compared to a simple binomial model wherein an event is defined to be a series of rainless days of desired length. Computer programs to perform the required calculations are then presented and compared as to complexity and operating characteristics. Finally, an example of applying both programs to real data is presented and further comparisons are drawn between the two techniques.