Data 606 Assignment 3
Joseph Simone
9/13/2019
Chapter 3 - Porbability
Libraries used:
library(knitr)## Warning: package 'knitr' was built under R version 3.5.3library(VennDiagram)## Warning: package 'VennDiagram' was built under R version 3.5.3## Loading required package: grid## Loading required package: futile.logger## Warning: package 'futile.logger' was built under R version 3.5.3library(png)
library(grid)
library(gmodels)## Warning: package 'gmodels' was built under R version 3.5.3library(openintro)## Please visit openintro.org for free statistics materials##
## Attaching package: 'openintro'## The following objects are masked from 'package:datasets':
##
## cars, treesDice Roll
imgage <- "C:/Users/jpsim/Documents/Stat & Probability for Data/1.png"
include_graphics(imgage)
a.There is not combinations a pair of dice being rolled will result in a sum of 1.
## Combinations: ((1,4),(2,3), (3,2), (4,1))
(4/36)## [1] 0.1111111#Combinations (6,6)
(1/36)## [1] 0.02777778Poverty and Language
imgage <- "C:/Users/jpsim/Documents/Stat & Probability for Data/2.png"
include_graphics(imgage)
a.There are 4.2% of people who fall into both living below the proverty line and speaking a foreign language, therefore, the answer is no.
venn <- draw.pairwise.venn(14.6, 20.7, 4.2, c("Foreing Language", "Povery"), scale = FALSE, fill = c("blue", "red"));
grid.draw(venn);
10.4 percent living below the poverty line and speak English at home
Poverty_foreign <- (14.6+20.7)-4.2
Poverty_foreign## [1] 31.1100 - Poverty_foreign## [1] 68.9Assortative Mating
imgage <- "C:/Users/jpsim/Documents/Stat & Probability for Data/3.png"
include_graphics(imgage)
am <- data.frame(assortive.mating)
am## self_male partner_female
## 1 blue blue
## 2 blue blue
## 3 blue blue
## 4 blue blue
## 5 blue blue
## 6 blue blue
## 7 blue blue
## 8 blue blue
## 9 blue blue
## 10 blue blue
## 11 blue blue
## 12 blue blue
## 13 blue blue
## 14 blue blue
## 15 blue blue
## 16 blue blue
## 17 blue blue
## 18 blue blue
## 19 blue blue
## 20 blue blue
## 21 blue blue
## 22 blue blue
## 23 blue blue
## 24 blue blue
## 25 blue blue
## 26 blue blue
## 27 blue blue
## 28 blue blue
## 29 blue blue
## 30 blue blue
## 31 blue blue
## 32 blue blue
## 33 blue blue
## 34 blue blue
## 35 blue blue
## 36 blue blue
## 37 blue blue
## 38 blue blue
## 39 blue blue
## 40 blue blue
## 41 blue blue
## 42 blue blue
## 43 blue blue
## 44 blue blue
## 45 blue blue
## 46 blue blue
## 47 blue blue
## 48 blue blue
## 49 blue blue
## 50 blue blue
## 51 blue blue
## 52 blue blue
## 53 blue blue
## 54 blue blue
## 55 blue blue
## 56 blue blue
## 57 blue blue
## 58 blue blue
## 59 blue blue
## 60 blue blue
## 61 blue blue
## 62 blue blue
## 63 blue blue
## 64 blue blue
## 65 blue blue
## 66 blue blue
## 67 blue blue
## 68 blue blue
## 69 blue blue
## 70 blue blue
## 71 blue blue
## 72 blue blue
## 73 blue blue
## 74 blue blue
## 75 blue blue
## 76 blue blue
## 77 blue blue
## 78 blue blue
## 79 blue brown
## 80 blue brown
## 81 blue brown
## 82 blue brown
## 83 blue brown
## 84 blue brown
## 85 blue brown
## 86 blue brown
## 87 blue brown
## 88 blue brown
## 89 blue brown
## 90 blue brown
## 91 blue brown
## 92 blue brown
## 93 blue brown
## 94 blue brown
## 95 blue brown
## 96 blue brown
## 97 blue brown
## 98 blue brown
## 99 blue brown
## 100 blue brown
## 101 blue brown
## 102 blue green
## 103 blue green
## 104 blue green
## 105 blue green
## 106 blue green
## 107 blue green
## 108 blue green
## 109 blue green
## 110 blue green
## 111 blue green
## 112 blue green
## 113 blue green
## 114 blue green
## 115 brown blue
## 116 brown blue
## 117 brown blue
## 118 brown blue
## 119 brown blue
## 120 brown blue
## 121 brown blue
## 122 brown blue
## 123 brown blue
## 124 brown blue
## 125 brown blue
## 126 brown blue
## 127 brown blue
## 128 brown blue
## 129 brown blue
## 130 brown blue
## 131 brown blue
## 132 brown blue
## 133 brown blue
## 134 brown brown
## 135 brown brown
## 136 brown brown
## 137 brown brown
## 138 brown brown
## 139 brown brown
## 140 brown brown
## 141 brown brown
## 142 brown brown
## 143 brown brown
## 144 brown brown
## 145 brown brown
## 146 brown brown
## 147 brown brown
## 148 brown brown
## 149 brown brown
## 150 brown brown
## 151 brown brown
## 152 brown brown
## 153 brown brown
## 154 brown brown
## 155 brown brown
## 156 brown brown
## 157 brown green
## 158 brown green
## 159 brown green
## 160 brown green
## 161 brown green
## 162 brown green
## 163 brown green
## 164 brown green
## 165 brown green
## 166 brown green
## 167 brown green
## 168 brown green
## 169 green blue
## 170 green blue
## 171 green blue
## 172 green blue
## 173 green blue
## 174 green blue
## 175 green blue
## 176 green blue
## 177 green blue
## 178 green blue
## 179 green blue
## 180 green brown
## 181 green brown
## 182 green brown
## 183 green brown
## 184 green brown
## 185 green brown
## 186 green brown
## 187 green brown
## 188 green brown
## 189 green green
## 190 green green
## 191 green green
## 192 green green
## 193 green green
## 194 green green
## 195 green green
## 196 green green
## 197 green green
## 198 green green
## 199 green green
## 200 green green
## 201 green green
## 202 green green
## 203 green green
## 204 green greenblue = subset(am, partner_female == "blue")
x = table(am$self_male, am$partner_female)
y = as.data.frame(x)
names(y)[1] = 'Self Male'
names(y)[2] = 'Partner Female'
y## Self Male Partner Female Freq
## 1 blue blue 78
## 2 brown blue 19
## 3 green blue 11
## 4 blue brown 23
## 5 brown brown 23
## 6 green brown 9
## 7 blue green 13
## 8 brown green 12
## 9 green green 16 ((sum(am$self_male =="blue")/nrow(am)) +
+ (sum(am$partner_female =="blue")/nrow(am)))- (sum(am$self_male =="blue" & am$partner_female=="blue")/nrow(am))## [1] 0.7058824 (sum(am$self_male =="blue" & am$partner_female=="blue")/nrow(am))/(sum(am$self_male=="blue")/nrow(am))## [1] 0.6842105(sum(am$self_male =="brown" & am$partner_female=="blue")/nrow(am))/(sum(am$self_male=="brown")/nrow(am))## [1] 0.3518519- The probability that a random self male from the study has a blue eyes is 56% and the probability of randomly select a partner female with blue eyes is 52.4% .Therefore, Both variables are dependent.
Books on a Bookshelf
imgage <- "C:/Users/jpsim/Documents/Stat & Probability for Data/4.png"
include_graphics(imgage)
bc <- data.frame(books)with(warpbreaks, CrossTable(bc$type, bc$format, prop.r = TRUE, prop.c = FALSE, prop.t = FALSE, prop.chisq = FALSE))##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## |-------------------------|
##
##
## Total Observations in Table: 95
##
##
## | bc$format
## bc$type | hardcover | paperback | Row Total |
## -------------|-----------|-----------|-----------|
## fiction | 13 | 59 | 72 |
## | 0.181 | 0.819 | 0.758 |
## -------------|-----------|-----------|-----------|
## nonfiction | 15 | 8 | 23 |
## | 0.652 | 0.348 | 0.242 |
## -------------|-----------|-----------|-----------|
## Column Total | 28 | 67 | 95 |
## -------------|-----------|-----------|-----------|
##
## (sum(bc$format=="hardcover"))/sum(table(bc)) *
(sum(bc$format=="paperback" & bc$type == "fiction"))/(sum(table(bc))-1)## [1] 0.1849944(sum(bc$type=="fiction"))/sum(table(bc)) *
(sum(bc$format=="hardcover"))/(sum(table(bc))-1)## [1] 0.2257559(sum(bc$type=="fiction"))/sum(table(bc)) *
(sum(bc$format=="hardcover"))/(sum(table(bc)))## [1] 0.2233795- Explain why this is the case. The larger the samples the smaller the difference.
Baggage fees
imgage <- "C:/Users/jpsim/Documents/Stat & Probability for Data/5.png"
include_graphics(imgage)
num_bags <- c('no-bags', 'one-bags', 'two-bags')
bag_fee <- c(0,25,35)
pass <- c(.54, .34, .12)
sample <- data.frame(num_bags, pass, bag_fee)
average_revenue <- (sum((sample$pass*sample$bag_fee))/sum(sample$pass))
average_revenue## [1] 12.7sqrt(0.54*(0-average_revenue)^2 + 0.34*(25-average_revenue)^2 + 0.12*(35-average_revenue)^2)## [1] 14.07871avg120flight <- (65*0 + 41*25 + 14 *25 + 14 * 35)
avg120flight## [1] 1865x <- c(0, 1025,840)
sqrt(sum((x-mean(x))^2/(length(x)-1)))## [1] 546.2676sd(x)## [1] 546.2676Income and gender
imgage <- "C:/Users/jpsim/Documents/Stat & Probability for Data/5.png"
include_graphics(imgage)
Income_range <- c("1 to $9999 or loss",
"10,000 to 14,999", "15, 000 to 24,999",
"25,000 to 34,999", "35,000 to 49,999",
"50,000 to 64,999", "65,000 to 74,999",
"75,000 to 99,999", "100,000 or more")
total <- c(.022, .047, 0.158, 0.183, 0.212, 0.139, 0.058, 0.084, 0.097)
x <- data.frame (Income_range, total)
x## Income_range total
## 1 1 to $9999 or loss 0.022
## 2 10,000 to 14,999 0.047
## 3 15, 000 to 24,999 0.158
## 4 25,000 to 34,999 0.183
## 5 35,000 to 49,999 0.212
## 6 50,000 to 64,999 0.139
## 7 65,000 to 74,999 0.058
## 8 75,000 to 99,999 0.084
## 9 100,000 or more 0.097barplot(total)
sum(x[1:5,2])## [1] 0.6220.622 * 0.41## [1] 0.25502- In conculsion, the assumption that was made in part C is wrong,it appears that like events are not independent.