Answers to Exercises

2.6

a) 0 as lowest possible sum is 2.

b) This can be obtained with 1+4, 4+1, 2+3, 3+2.

4/36
## [1] 0.1111111

c) Only if we get 6 on each dice.

1/36
## [1] 0.02777778

2.8

a) No there are 4.2% who are in both poor and foreign language spearkers.

b)

library(venneuler)
## Loading required package: rJava
MyVenn <- venneuler(c(Poor=146, Foreign=207,"Poor&Foreign"=42))
                    
MyVenn$labels <- c("Poor\n14.6","Foreign\n20.7")
plot(MyVenn)

c)

14.6-4.2
## [1] 10.4

d)

14.6+20.7-4.2
## [1] 31.1

e)

1-(14.6+20.7-4.2)
## [1] -30.1

f) P(Poverty)*P(Foreign)=3.02 which is not same as P(Poverty&Foreign)=4.2 so they are not independent

(20.7*14.6)/100
## [1] 3.0222

2.20

a) Blue eyes

(114+108-78)/204
## [1] 0.7058824

b)

78/114
## [1] 0.6842105

c)

23/54
## [1] 0.4259259
11/36
## [1] 0.3055556

d) No they don’t appear to be indepdendent as for each category the highest values correspond to when eyes of both the partners are of same color.

2.30

a)

28/95 * 59/94
## [1] 0.1849944

b)

28/95 * 59/94
## [1] 0.1849944

c)

28/95 * 59/95
## [1] 0.1830471

d) Because the difference if only of replacement of only 1 book in context of a population of 95. However if we were to withdraw multiple books, then the difference would be much more stark.

2.38

a) Probability model, avg revenue and SD

Model : E(x) = P(OnlyOneBag)X$25 + P(TwoBags)X($25+$30)

Avg Revenue :

mu <- 0.34*25+0.12*(25+30)
mu
## [1] 15.1

SD

var <- 0.54*(0-mu)^2 + 0.34 * (25-mu)^2 + 0.12 * (35-mu)^2
sqrt(var)
## [1] 14.28181

2.44

a) The distribution seems to be normally distributed with mean in range of $35000 to $49999.

b)

below50K<-2.2+4.7+15.8+18.3+21.2
below50K
## [1] 62.2

c) we are assuming that number of females and males are distributed with same proportions in each income group.

below50KFemale <- below50K * 0.41
below50KFemale
## [1] 25.502

d) Assumption made in c is not correct as per that percentage of females below 50K is only 62% which is significantly below the provided values of 72%

below50KFemale / 0.41
## [1] 62.2