Homework

2.6) a) 0, the lowest number we can get when we roll a pair of fair dices will be 2, not 1, so it will never happen. b) We can get the following combinations: 1 and 4, 4 and 1, 2 and 3, 3 and 2. Each combination can occur 1/61/6=1/36. 41/36 or 1/9 or 0.11111(1). c) The only combination we can get will be 6 and 6. Probability to get it will be 1/36 or 0.2777(7).

2.8) a) These events are not disjoint, a person can live below poverty and speak a foreign language at home. Actually it is stated that 4.2% fall into that category b) Please find the diagram below:

#install.packages('VennDiagram')

library(VennDiagram)
## Loading required package: grid
## Loading required package: futile.logger
grid.newpage()

draw.pairwise.venn(area1 = 14.6, area2 = 20.7, cross.area = 4.2, category = c("Below the poverty line", "A language other than English"))

## (polygon[GRID.polygon.1], polygon[GRID.polygon.2], polygon[GRID.polygon.3], polygon[GRID.polygon.4], text[GRID.text.5], text[GRID.text.6], text[GRID.text.7], text[GRID.text.8], text[GRID.text.9])
  1. It will be 14.6-4.2=10.4 (precent who lives below pov. minus (who do not speak English & live below poverty)).
  2. it will be 14.6+20.7-4.2=31.1 (prec. who lives below pov. plus who do not speak English minus (who do not speak English & live below poverty)).
  3. It will be 100-14.6-20.7+4.2=69.9 (all americans minus below pov. minus do not speak English + (who do not speak English & live below poverty)).
  4. No, if we multiply 0.146 by 0.207 we get 0.030222 which is not equal to 0.042.

2.20) a) (114+19+11)/204=144/204=0.70588235. b) 78/114=0.68421053. c) 19/54=0.35185185; 11/36=0.30555556. d) No, they are dependant. If multiply (114/204)x(108/204) we get 0.29584775 which not equal to 78/204=0.38235294.

2.30) a) (28/95)x(59/94)=0.1849944. b) (13/95)x(27/94)+(59/95)x(28/94)=0.03930571+0.1849944=0.22430011. c) (72/95)x(28/95)=0.22575588. d)The reason is that only one out of 95 books got effected and that one book will only make a difference of ~ one third of the samples (28 out 95).

2.38) a) mean or average revenue will be 0.34x25+0.12x60=15.7; standard deviation will be ((0-15.7)2x0.54+(25-15.7)2*0.34+(60-15.7)2x0.12)0.5=19.95019. b) Revenue could expect to be on average 120x15.7=1,901. Standard deviation 120^0.5x19.95019=218.5434.

2.44) a) It is normal or near normal. b) (2.2+4.7+15.8+18.3+21.2)=62.2. c) not enough data, but more than 0.622x0.41=0.25502; more than 0.25502, due to known fact that females make less than male in the USA. d) 0.718x0.41=0.29438. So, I was right that it is more than 0.25502. —