2.6

a) 0

b) 5 combinations = 5/36

c) 1/36

2.8

a) Not disjoint because some Americans have both characteristics

b)

library(VennDiagram)
## Loading required package: grid
## Loading required package: futile.logger
plot <-draw.pairwise.venn(20.7,14.6,4.2, c("Other language", "Poverty"), fill = c("green", "yellow"))
grid.draw(plot)

c) 14.6 - 4.2 = 10.4

d) Equal to the union of these events = 14.6 + 20.7 - 4.2 = 31.1

e) Equal to the complement of P union L or 1 - P union L or -30.1

f) These events are not independant because they do not follow the multiplication rule. If they were independant, their intersection would have probability of about 3%

2.20

a) (114 + 19 + 11)/204 = 0.7058824

b) = males with blues and partner with blue eyes / males with blue eyes = 78/108 = 0.7222222

c) 23/55 = 0.4181818

d It does not appear eye colors of male respondants and their partner are independant. Over half the respondants half the same color eyes, whereas if they were indpendant, this should be about 1/3 of respondants.

2.30

a) (28/95)x(59/94) = 0.1849944

b) (59/95)x(28/94) + (13/95)x(27/94) = 0.2243001

c) (72/95)x(28/95) = 0.2233795

d) Replacement has little effect when the sample size is large and only two samples are taken

2.38

a) E[revenue] = .34 x 25 + .12 x (25 + 35) = 15.7

\[Var(rev)\quad =\quad E\left[ { Rev }^{ 2 } \right] \quad -{ E\left[ Rev \right] }^{ 2 }\quad =\quad \] 398.01

b) We assume luggage revene for each passenger is IID Expected value = 1884

\[{Var } = { N }^{ 2 }\bullet Var(rev) =\]

5.73134410^{6}

2.44

a) The distribution appears to be somewhat right skewed

b) 62.2%

c) 25.5%, assuming income is independant of gender, an assumption that isn’t true

d) This indicates the indepedance assumption was false