# 1. Introduction

## a. define a random variable, an outcome, an event, mutually exclusive events, and exhaustive events;

## b. state the two defining properties of probability and distinguish among empirical, subjective, and a priori probabilities;

## c. state the probability of an event in terms of odds for and against the event;

In probability, what is an experiment?

The act of making an observation or taking a measurement

What is the result of an experiment called?

An outcome

What are mutually exclusive events?

Events that occur one at a time. E.g. rolling dice. Odds and evens are mutually exclusive because you'll never get them at the same time

What are exhaustive events?

Events that cover all the possibilities. In rolling a dice, odds and evens are an exhaustive list because there can be no other possibilities

What does `P(E)`

stand for and what are its two defining properties?

- `P(E)`

= Probability that an event will happen

1. `0 <= P(E) <= 1`

= a probability will always be between 0 and 1. It is expressed as a percentage.

2. The sum of probabilities of exhaustive and mutually exclusive events will always equal one.

What is empirical probability?

Empirical probability is a probability based on relative frequency of occurrence and is only accurate if data relationships are stable over time.

What is priori probability?

Priori probability is a probability based on logical analysis rather than observation or personal judgment. For example, when you toss dice fairly, the probability of rolling an even number is 50%.

What is subjective probability?

Subjective probability is a probability based on personal or subjective judgment. For example, based on his own judgment, Bill believes that the probability that IBM's revenue will increase in 2005 is 60%.

What is the Dutch Book Theorem?

- It says that inconsistent probabilities create opportunities for profit.

- E.g.

- If event E causes both security A and B to rise, but only A has the possibility priced in, and B does not, then

- If E does occur, the price of A will not rise as much as B because E is already incorporated into the price of A

- If E does not occur, the price of A will fall farther than B because it was overvalued in the first place (in anticipation of E happening)

What is the "pairs arbitrage trade"?

According to the Dutch Book Theorem, if event E will move both asset A and B, and only asset A has the possibility of E priced in, while B does not, then

- The "pairs arbitrage trade" is to go long on B and go short on A.

- This way, if the event happens:

- A will not go up much so you don't lose your money on the short

- B will go up so you make money on the long

- If the event does not happen

- A will fall because it was overpriced, you make money on the short

- B will not fall as far because E was not priced in

##### Source:

- CFA