Let R be a finite noncommutative ring. Show that the probability that two randomly chosen elements from R commute is at most 5/8. [Hint: Mimic the group case and use the fact that the additive group R/C(R) is not cyclic.]

Week 7 Lecture 7 March 8th, 2017 Review: Population and Sample Researchers often want to answer questions about some large groups of individuals. (This group is called the population.) Often the researchers cannot measure (or survey) all individuals in the population, so they measure a subset of individuals that is chosen to represent the entire population. (This subset is called a sample.) A sample design describes exactly how to choose a sample from the population The researchers then use statistical techniques (Called statistical inference) to make conclusions about the population based on the sample Choosing a Representative Sample Samp