 These contents were constructed based on the actual lectures of Prof. Nakamura. Lecture video for RealPlayer (opening only)

### Message to students (Nakamura):

The thinking of probability theory helps in understanding social, economic, and

scientific objects of uncertainty which span a variety of fields. It is unusual to find

a field of study whose applications are so widespread. Probability theory is also

called the science of proportions. It deals not only with uncertain events, but it

can also treat area, counts, and amounts of items. Therefore, it is also useful when

we consider the work of databases or processing of images and patterns. We assume

here that the student has knowledge of simple logic theory and set theory. It is

said that set theory type of probability theory was created by the Russian mathematical

scholar Kolmogorov (more precisely, measure theory type probability theory). There are

various schools of thought in probability theory, but here we will focus on set theory

type of thinking. The objective for this is not to be able to merely do probability

calculations, but rather we hope that students will eventually be able to mathematically

model the nature of the targets of study. Some of the tests are more difficult than they

seem at first glance, but if you think them over carefully, they are designed to help

you understand the basic concepts of the chapter. Also, you may use programmable

calculators with functions, but it would also be good to have your own simple to use

programming environment such as Basic or Perl (at times like this, interpreted languages

are convenient).

Each of the chapters below contains the contents for one (90 minute) lecture.

## Index

Chapter 1 Events

Chapter 2 Probability

Chapter 3 Conditional probability/joint probability

Chapter 5 Moment

Chapter 6 Distribution functions/probability density functions

Chapter 7 Joint probability density

Chapter 8 Concrete distributions

Chapter 9 Law of Large Numbers