b:head_first_statistics:using_discrete_probability_distributions
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| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| b:head_first_statistics:using_discrete_probability_distributions [2023/10/02 06:11] – [e.gs in R] hkimscil | b:head_first_statistics:using_discrete_probability_distributions [2023/10/04 10:29] (current) – old revision restored (2023/10/04 10:18) hkimscil | ||
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| \begin{align*} | \begin{align*} | ||
| & E[(X + Y)^2] = E[X^2 + 2XY + Y^2] = E[X^2] + 2E[XY] + E[Y^2] \\ | & E[(X + Y)^2] = E[X^2 + 2XY + Y^2] = E[X^2] + 2E[XY] + E[Y^2] \\ | ||
| - | - & [E(X + Y)]^2 = [E(X) + E(Y)]^2 = E(X)^2 + 2E(X)E(Y) + E(Y^2) \\ | + | - & [E(X + Y)]^2 = [E(X) + E(Y)]^2 = E(X)^2 + 2E(X)E(Y) + E(Y)^2 \\ |
| \end{align*} | \end{align*} | ||
| Line 624: | Line 624: | ||
| Var[(X+Y)] = | Var[(X+Y)] = | ||
| & E[X^2] & + & 2E[XY] & + & E[Y^2] \\ | & E[X^2] & + & 2E[XY] & + & E[Y^2] \\ | ||
| - | - & E(X)^2 & - & 2E(X)E(Y) & - & E(Y^2) \\ | + | - & E(X)^2 & - & 2E(X)E(Y) & - & E(Y)^2 \\ |
| & Var[X] & + & 2 E[XY]-2E(X)E(Y) & + & Var[Y] \\ | & Var[X] & + & 2 E[XY]-2E(X)E(Y) & + & Var[Y] \\ | ||
| \end{align*} | \end{align*} | ||
b/head_first_statistics/using_discrete_probability_distributions.txt · Last modified: 2023/10/04 10:29 by hkimscil