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--- b:head_first_statistics:using_discrete_probability_distributions [2019/10/10 18:35] – [Fat Dan changed his prices] hkimscil
+++ b:head_first_statistics:using_discrete_probability_distributions [2019/10/14 03:49] – [Fat Dan changed his prices] hkimscil
@@ Line 384: / Line 384: @@
 Var(X + Y) & = & Var(X) + Var(Y) \\
 E(X - Y) & = & E(X) - E(Y) \\
-Var(X - Y) & = & Var(X) - Var(Y) \\
+Var(X - Y) & = & Var(X) + Var(Y) \\
 E(aX + bY) & = & aE(X) + bE(Y)  \\
 Var(aX + bY) & = & a^{2}Var(X) + b^{2}Var(Y) \\
 E(aX - bY) & = & aE(X) - bE(Y)  \\
-Var(aX - bY) & = & a^{2}Var(X) - b^{2}Var(Y) \\
+Var(aX - bY) & = & a^{2}Var(X) + b^{2}Var(Y) \\
 \end{eqnarray*}
+----
+A restaurant offers two menus, one for weekdays and the other for weekends. Each menu offers four set prices, and the probability distributions for the amount someone pays is as follows:
 | Weekday:  |||||
@@ Line 398: / Line 401: @@
 | y  | 15  | 20  | 25  | 30  |
 | P(Y = y)  | 0.15  | 0.6  | 0.2  | 0.05  |
+Who would you expect to pay the restaurant most: a group of 20 eating at the weekend, or a group of 25 eating on a weekday?
+<code>
+x1 <- c(10,15,20,25)
+x1p <- c(.2,.5,.2,.1)
+x2 <- c(15,20,25,30)
+x2p <- c(.15,.6,.2,.05)
+x1n <- 25
+x2n <- 20
+x1mu <- sum(x1*x1p)
+x2mu <- sum(x2*x2p)
+x1e <- x1mu*x1num
+x2e <- x2mu*x2num
+x1e
+x2e
+</code>
+<code>> x1e
+[1] 400
+> x2e
+[1] 415
+> </code>
+x2e will spend more.
+====== e.g. ======
+| Restaurant A:   |||||
+| x  | 20  | 30  | 40  | 45  |
+| P(X = x)  | 0.3  | 0.4  | 0.2  | 0.1  |
+| Restaurant B:   ||||
+| y  | 10  | 15  | 18  |
+| P(Y = y)  | 0.2  | 0.6  | 0.2  |