Statistical Notation¶
Going forward we will use some notation to clean up our equations.
For a data set of values for a variable \(x\), \(x_i\) (\(i = 1, 2, 3, \dots, N\)):
Expected value of \(f(x)\) (which can be considered the average of \(f(x)\)):
\[ \langle f(x) \rangle = \frac{1}{N} \sum_{i=1}^{N} f(x_i) \]Expected value of \(x\) is the mean of the data set:
\[ \langle x \rangle = \frac{1}{N} \sum_{i=1}^{N} x_i \]Standard deviation (which is an indication of the spread of the data):
\[ \sigma = \sqrt{\frac{\sum_{i=1}^{N} (x_i - \langle x \rangle)^2}{N}} \]