# This assignment looks at retail data supplied by an anonymous Belgian retail supermarket store. The data are collected over three non-consecutive periods. This results in approximately 5 months of data. The total amount of receipts being collected equals 88,162. Over the entire data collection period, the supermarket store carries 16,470 unique SKUs (Stock Keeping Units). In total, 5,133 customers have purchased at least one product in the supermarket during the data collection period.

# 1- Install and load in the arules library.
library("arules")
library("arulesViz")
# 2- Load in the data using the following command:
retail <- read.transactions("retail.dat")

# 3- Create a summary of this data (hint: summary(retail)). What does this summary indicate?
summary(retail)
## transactions as itemMatrix in sparse format with
## 88162 rows (elements/itemsets/transactions) and
## 16470 columns (items) and a density of 0.0006257289
##
## most frequent items:
## 39 48 38 32 41 (Other)
## 50675 42135 15596 15167 14945 770058
##
## element (itemset/transaction) length distribution:
## sizes
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
## 3016 5516 6919 7210 6814 6163 5746 5143 4660 4086 3751 3285 2866 2620 2310
## 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
## 2115 1874 1645 1469 1290 1205 981 887 819 684 586 582 472 480 355
## 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
## 310 303 272 234 194 136 153 123 115 112 76 66 71 60 50
## 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
## 44 37 37 33 22 24 21 21 10 11 10 9 11 4 9
## 61 62 63 64 65 66 67 68 71 73 74 76
## 7 4 5 2 2 5 3 3 1 1 1 1
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.00 4.00 8.00 10.31 14.00 76.00

In n rolls of a fair die, let X be the number of times 1 is rolled,...