expected_value_and_variance_properties
Differences
This shows you the differences between two versions of the page.
| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| expected_value_and_variance_properties [2023/10/04 13:05] – [e.gs in R] hkimscil | expected_value_and_variance_properties [2023/12/07 12:18] (current) – [Theorem 2: Why square] hkimscil | ||
|---|---|---|---|
| Line 33: | Line 33: | ||
| \begin{align*} | \begin{align*} | ||
| - | Var[aX] & = & E[a^2X^2] − (E[aX])^2 \\ | + | Var[aX] & = E[a^2X^2] − (E[aX])^2 \\ |
| - | & = & a^2 E[X^2] - (a E[X])^2 \\ | + | & = a^2 E[X^2] - (a E[X])^2 \\ |
| - | & = & a^2 E[X^2] - (a^2 E[X]^2) \\ | + | & = a^2 E[X^2] - (a^2 E[X]^2) \\ |
| - | & = & a^2 (E[X^2] - (E[X])^2) \\ | + | & = a^2 (E[X^2] - (E[X])^2) \\ |
| - | & = & a^2 (Var[X]) \label{var.theorem.2} \tag{variance theorem 2} \\ | + | & = a^2 (Var[X]) \label{var.theorem.2} \tag{variance theorem 2} \\ |
| \end{align*} | \end{align*} | ||
| ====== Theorem 3: Why Var[X+c] = Var[X] ====== | ====== Theorem 3: Why Var[X+c] = Var[X] ====== | ||
expected_value_and_variance_properties.1696392309.txt.gz · Last modified: 2023/10/04 13:05 by hkimscil