Random Variables

Most of the variables that exist in finance can be defined by an implied future value.
This future value is calculated based on historical probability and the liklihood of different outcomes.
This can be defined as dealing with random variables
These are variables whose value is determined by the outcome of a random process.
The outcome of an experiment need not be a number, for example, the outcome when a coin is tossed can be 'heads' or 'tails'.
This outcome can either be:

Discrete - indicating a finite number of possible values
Continuous - indicating an infinite number of possible values

A random variable is a function that associates a unique numerical value with every outcome of an experiment.
The value of the random variable will vary from trial to trial as the experiment is repeated.

A random variable is a variable for which a probability can be assigned to the outcome variable.
There are two types of random variable:
Discrete Random Variable - Every outcome has a specific probability
Continuous Random Variable - There are an infinite number of outcomes

Examples of Discrete

Rolling a Dice
Picking a Card from a Pack
Throwing a Coin

Examples of Continuous

Stock price in 1 years time

Although there are an infinite number of possible values past experience and historical data can help us to assess the liklihood of different values.

Population vs Sample

Population - a complete set of observations on a variable
Sample - a subset of observations on a variable

The main reason for working with a sample is obvious
It will cost less than trying to work with the whole population
You are able to make inferences about what is going on in the population

Random Walk

A random variable is a type of measurement taken on the outcome of a random experiment.

A random variable is a function that maps each outcome (w) in the sample space (?) into a set of real numbers.

Examples are:
throwing a nice
coin toss
card example
N points on a circle