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--- b:head_first_statistics:using_discrete_probability_distributions [2024/09/29 23:29] – [Fat Dan changed his prices] hkimscil
+++ b:head_first_statistics:using_discrete_probability_distributions [2024/10/01 21:44] (current) – [Fat Dan changed his prices] hkimscil
@@ Line 283: / Line 283: @@
 \begin{eqnarray*}
-\text {original win & = & c(0, 5, 10, 15, 20)} \\
+\text {original win} & = & \text {c(0, 5, 10, 15, 20)} \\
-\text {original cost & = & c(1)} \\
+\text {original cost} & = & \text {c(1)} \\
-\text {X & = & the amount of money you receive} \\
+\text {X} & = & \text {the amount of money you receive} \\
 \end{eqnarray*}
@@ Line 301: / Line 301: @@
 E(X) = -.77 and E(Y) = -.85. What is 5 * E(X) + 3?
-$ 5 * E(X) = -3.85 $
+\begin{eqnarray*}
-$ 5 * E(X) + 3 = -0.85 $
+E(X) & = & -.77 \\
-$ E(Y) = 5 * E(X) + 3 $
+E(Y) & = & E(5X+3) \;\;\;\;\;  \because Y=5X+3 \\
+& = & E(5X) + 3 \\
+& = & 5 E(X) + 3 \\
+& = & -0.85 \\
+\\
+\\
+Var(Y) & = & Var(5X+3) \\
+& = & Var(5X) + Var(3) \\
+& = & Var(5X) \\
+& = & 5^2 Var(X) \\
+& = & 67.4275
+\end{eqnarray*}
-$ 5 * Var(X) = 13.4855 $
-$ 5^2 * Var(X) = 67.4275 $
-$ Var(Y) = 5^2 * Var(X) $
 \begin{eqnarray*}
@@ Line 381: / Line 388: @@
 </code>
-그런데
+위는 각각 계산한 것. 아래는 Y = X - 0.5를 적용해서 계산한 것
 \begin{eqnarray*}
 E(X-a) & = & E(X) - a \\