Module 3 - Fitting Discrete Distributions 1

Report

library(readr)
data <- read_csv("C:/Users/gmutya048/Downloads/data.csv")

## 
## -- Column specification -----------------------------------------------------------------------------------
## cols(
##   `roll 1` = col_double(),
##   `roll 2` = col_double(),
##   `roll 3` = col_double(),
##   `roll 4` = col_double(),
##   `roll 5` = col_double(),
##   `roll 6` = col_double(),
##   `roll 7` = col_double(),
##   `roll 8` = col_double(),
##   `roll 9` = col_double(),
##   `roll 10` = col_double(),
##   `roll 11` = col_double(),
##   `roll 12` = col_double()
## )

Find the maximum dice size: 20

max(data, na.rm = TRUE)

## [1] 20

Find the group size: 12

library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

ncol(data)

## [1] 12

Considering a roll of 1/2/3 to be a success, find the number of successes per grouping.

Number of successes when rolling a 20 sided dice in groups of 12.

library(dplyr)
freq = array(12)
for(i in 1:12){
 freq[i] = 0
}
for(row in 1:nrow(data)){
  count = 0
  for(n in data[row,]){
    for(i in n){
      if(n<4)
        count = count + 1
    }
  }
  freq[count] = freq[count] + 1
}

matrix(
  freq,
  nrow = 1,
  byrow = TRUE,
  dimnames = list(
    c("successes "),
    c(1:12)
  )
)

##               1    2    3    4   5  6  7 8 9 10 11 12
## successes  6473 6339 3723 1502 469 97 11 1 0  0  0  0

plot(freq, bty="o", main = "Number of successes when rolling a 20 sided dice in groups of 12",ylab="count",xlab=" Number of successes")

Analysis

1. The dice roll is believed to be (not)fair because data is not in normally distributed.

2. The distribution observed in the plot appears to be right skewed or Positive-skew distribution.