Mathematical Notation

Notation is a common language used to communicate mathematical ideas. Think of notation as a universal language used by academic and industry professionals to convey mathematical ideas.

Random Variables

A placeholder for the possible value of some process. (Notation = \(x\))

In a spreadsheet each column is associated with a random variable.

Capital vs Lower

Consider we have a spreadsheet containing column of How much time a visitor stay on a website.

\(X\) : Amount of Time on website. The entire set of possible values.

\(x\) : A placeholder for any possible value.

When look at an individual outcome of our random variable, we signify this with a lowercase letter \(x\). Often the lowercase letter has a subscript \(x_n\) that attach notation to each specific value in our dataset.

• Random Variable is notated by capital letter \(X\)

• Observed Value is notated by lowercase letter \(x_1\)

We might imagine the Random Variables as columns in our dataset, while a particular value will be in a specific row.

Mean Notation

$$\bar{x}\ = \frac{1}{n}\sum_{i = 1}^{n}(x_i)$$

Aggregation

An aggregation is a way to turn multiple numbers into fewer numbers (commonly one number).

Summation is a common aggregation. The notation used to sum our values is a greek symbol called Sigma \(\sum\)