Conditional Probability, Bayes’ Rule, and Independence
1.10.1. Conditional Probability Consider a statistical experiment with probability space { ^, &, P}, and suppose it is known that the outcome of this experiment is contained in a set …
Quality Control
1.2.1. Sampling without Replacement As a second example, consider the following case. Suppose you are in charge of quality control in a light bulb factory. Each day N light bulbs …
Bayes’ Rule
Let A and B be sets in &. Because the sets A and A form a partition of the sample space ^, we have B = (B П A) U …
Quality Control in Practice
The problem in applying this result in quality control is that K is unknown. Therefore, in practice the following decision rule as to whether K < R or not is …
Sampling with Replacement
As a third example, consider the quality control example in the previous section except that now the light bulbs are sampled with replacement: After a bulb is tested, it is …
Why Do We Need Sigma-Algebras of Events?
In principle we could define a probability measure on an algebra Ж of subsets of the sample space rather than on a a-algebra. We only need to change condition (1.10) …
Properties of Algebras and Sigma-Algebras
1.4.1. General Properties In this section I will review the most important results regarding algebras, a - algebras, and probability measures. Our first result is trivial: Theorem 1.1: If an …
