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--- b:head_first_statistics:using_discrete_probability_distributions [2025/09/24 07:16] – [Expectation gives you . . .] hkimscil
+++ b:head_first_statistics:using_discrete_probability_distributions [2025/09/25 07:04] (current) – [확률의 연산] hkimscil
@@ Line 49: / Line 49: @@
 $$ E(X) = \sum{k * P(X=x)} $$
-| Combination  | None   | Lemons  | Cherries  | Dollars/cherry  | Dollars   |
+| Combination  | None   | Lemons  | Cherries  | Dollars/cherry  | Dollars   |  |
-| k         | -1  | 4   | 9     | 14         | 19    |
+| k         | -1  | 4   | 9     | 14         | 19    |  |
-| P(X=x)  | 0.977  | 0.008   | 0.008     | 0.006           | 0.001     |
+| P(X=x)  | 0.977  | 0.008   | 0.008     | 0.006           | 0.001     |  |
-| E(X)    | -0.977  | 4*0.008    | 9**0.008    | 14*0.006    | 19*0.001       |
+| E(X)    | -0.977  | 4*0.008    | 9**0.008    | 14*0.006    | 19*0.001     |  |
-|         | -0.977  | 0.032  | 0.072   | 0.084  | 0.019    |
+|         | -0.977  | 0.032  | 0.072   | 0.084  | 0.019    | $\sum = -0.77 $  |
 $$E(X) = -0.77$$
@@ Line 318: / Line 318: @@
 ===== 확률의 연산 =====
+SEE [[:Expected value and variance properties]]
 \begin{eqnarray*}
@@ Line 324: / Line 325: @@
 E(X + Y) & = & E(X) + E(Y) \\
 Var(X + Y) & = & Var(X) + Var(Y) \\
-\end{eqnarray*}
+\\
-\begin{eqnarray*}
 E(X1 + X2 + \ldots Xn) & = & nE(X) \\
 Var(X1 + X2 + \ldots Xn) & = & nVar(X) \\
-\\
+\text{c.f., } \;\;
+Var(X1 + X1 + X1) & = & 9 * Var(X)\\
 \end{eqnarray*}