Mathematical Notation
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.
| Time | $X$ |
| 5 | \(x_1\) |
| 10 | \(x_2\) |
| ... | ... |
| ... | ... |
| n | \(x_n\) |
$X$ : 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 \(\sum\)