دانلود کتاب تحلیل کمی – بخش 2 کتاب 1 (FRM Part 1)

Probability theory is the foundation of statistics, econometrics, and risk management. This chapter introduces probability in its simplest form. A probability measures the likelihood that some event occurs. In most financial applications of probability, events are tightly coupled with numeric values. Examples of such events include the loss on a portfolio, the number of defaults in a mortgage pool, or the sensitivity of a portfolio’s value to a rise in short-term interest rates. Events can also be measured by values without a natural numeric correspondence. These include categorical variables, such as the type of a financial institution or the rating on a corporate bond. Probability is introduced through three fundamental principles.
1. The probability of any event is non-negative.
2. The sum of the probabilities across all outcomes is one.
3. The joint probability of two independent events is the product of the probability of each.
This chapter also introduces conditional probability, an important concept that assigns probabilities within a subset of all events. After that, the chapter moves on to discuss independence and conditional independence. It concludes by examining Bayes’ rule, which provides a simple yet powerful expression for incorporating new information or data into probability estimates.