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--- b:head_first_statistics:using_discrete_probability_distributions [2019/10/14 01:42] – [Fat Dan changed his prices] hkimscil
+++ b:head_first_statistics:using_discrete_probability_distributions [2019/10/15 02:45] – hkimscil
@@ Line 421: / Line 421: @@
 x2e
 </code>
+<code>> x1e
+[1] 400
+> x2e
+[1] 415
+> </code>
 x2e will spend more.
+====== e.g. ======
+<WRAP box>
+Sam likes to eat out at two restaurants. Restaurant A is generally more expensive than
+restaurant B, but the food quality is generally much better.
+Below you’ll find two probability distributions detailing how much Sam tends to spend at each
+restaurant. As a general rule, what would you say is the difference in price between the two
+restaurants? What’s the variance of this?
+</WRAP>
+| 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  |
+<code>
+x3 <- c(20,30,40,45)
+x3p <- c(.3,.4,.2,.1)
+x4 <- c(10,15,18)
+x4p <- c(.2,.6,.2)
+x3e <- sum(x3*x3p)
+x4e <- sum(x4*x4p)
+x3e
+x4e
+## difference in price between the two
+x3e-x4e
+x3var <- sum(((x3-x3e)^2)*x3p)
+x4var <- sum(((x4-x4e)^2)*x4p)
+x3var
+x4var
+## difference in variance between the two
+## == variance range
+x3var+x4var
+</code>
+<code>
+> x3 <- c(20,30,40,45)
+> x3p <- c(.3,.4,.2,.1)
+> x4 <- c(10,15,18)
+> x4p <- c(.2,.6,.2)
+>
+> x3e <- sum(x3*x3p)
+> x4e <- sum(x4*x4p)
+>
+> x3e
+[1] 30.5
+> x4e
+[1] 14.6
+> ## difference in price between the two
+> x3e-x4e
+[1] 15.9
+>
+>
+> x3var <- sum(((x3-x3e)^2)*x3p)
+> x4var <- sum(((x4-x4e)^2)*x4p)
+>
+> x3var
+[1] 72.25
+> x4var
+[1] 6.64
+> ## difference in variance between the two
+> ## == variance range
+> x3var+x4var
+[1] 78.89
+</code>
+====== e.g. ======