Probability-theoretic investigations on inheritance, XII-2. Probability of paternity

Paternity exclusion and probability of paternity.

The principles of paternity exclusion and current systems of paternity testing are reviewed. Recent advances, especially the utilization of human leukocyte antigens (HLA), have greatly improved the likelihood of exclusion of the innocent accused male. Failure to exclude an alleged father through multiple test systems increases the suspicion that he is the biological father. This can be expresse...

Measure Theoretic Probability

Preface In these notes we explain the measure theoretic foundations of modern probability. The notes are used during a course that had as one of its principal aims a swift introduction to measure theory as far as it is needed in modern probability, e.g. to define concepts as conditional expectation and to prove limit theorems for martingales. Everyone with a basic notion of mathematics and prob...

Measure-Theoretic Probability I

Prequential probability: game-theoretic = measure theoretic

This article continues study of the prequential framework for evaluating a probability forecaster. Testing the hypothesis that the sequence of forecasts issued by the forecaster is in agreement with the observed outcomes can be done using prequential notions of probability. It turns out that there are two natural notions of probability in the prequential framework: game-theoretic, whose idea go...

on the probability of being a 2-engel group

‎let $g$ be a finite group and $d_2(g)$ denotes the probability ‎that $[x,y,y]=1$ for randomly chosen elements $x,y$ of $g$‎. ‎we ‎will obtain lower and upper bounds for $d_2(g)$ in the case where ‎the sets $e_g(x)={yin g:[y,x,x]=1}$ are subgroups of $g$ for ‎all $xin g$‎. ‎also the given examples illustrate that all the ‎bounds are sharp.