TABLE OF CONTENTS This chapter discusses the basics of probability and statistics. It is intended for readers who have a need for an introduction to this topic, or an accelerated review of it. Readers with a strong background in probability and statistics may skip this chapter. Others will find it useful, as well as a convenient source for review.
Probability and statistics are two closely related branches of mathematics. They apply to all science and engineering fields, sociology, business, education, insurance, and many others. For this reason, we devote all subsequent chapters to this topic.
In some cases, measurements of various parameters are deterministic; this means that the results can be predicted exactly. However, in most cases there are many unpredictable variables involved, and it becomes an impossible task to predict the result exactly. Consider, for example, the case of a radar system detection, where the radar system detects the presence of a target and extracts useful information such as range (distance) and range rate (velocity) of the target. Here, we are confronted with probabilities such as:
the probability of false alarm, that is, the probability that the radar receiver decides that a target is present when in fact it is not present.
the probability of detection, that is, the probability that the radar receiver decides a target is present when in fact it is present.
Obviously, we need to use a mathematical procedure to analyze such situations. This mathematical procedure is the field of...
