DAT 605 - Wk5, Discussion 5

CHAPTER 1. DISCRETE PROBABILITY DISTRIBUTIONS Page 12

• First let fix the convention:

0 = Tails and 1 = Heads

library(matlib)
library(MASS)
library(dplyr)
library(ggplot2)

# Function to Randomly perform coin toss
CoinToss <- function(n=10){ 
  e <- sample(0:1,n,rep=T)
  e0 <- sum(e==0)
  print("The no. of Tails :")
  print(e0)
  
  print("The probability of Tails :")
  print(round(e0/n,2))

  e1 <- sum(e ==1)
  print("The no. of Heads :")
  print(e1)
  
  print("The probability of Heads :")
  print(round(e1/n,2))
  
  df <- data.frame(e0,e1,e)
  dfnew <-df %>% rename(Tails=e0, Heads=e1, Outcome = e)
  dfnew1 <- dfnew %>% mutate(Outcome = ifelse(Outcome==0,"Tails", ifelse(Outcome ==1, "Heads", NA)))
  


  #plot histogram of OUtcomes
  ggplot(data = dfnew1) + 
  geom_bar(mapping = aes(x = Outcome, y = ..prop.., group = 1), stat = "count") + 
  scale_y_continuous(labels = scales::percent_format())

  
}

To empirically test the outcomes by increasing the no. of coin tosses

Observations:

• As can be seen, the probabilities approaches half or 50% as no. of coin tosses increases from 10 to 1 million

# Ten coin tosses
CoinToss(10)

## [1] "The no. of Tails :"
## [1] 4
## [1] "The probability of Tails :"
## [1] 0.4
## [1] "The no. of Heads :"
## [1] 6
## [1] "The probability of Heads :"
## [1] 0.6

# Fifty coin tosses
CoinToss(50)

## [1] "The no. of Tails :"
## [1] 20
## [1] "The probability of Tails :"
## [1] 0.4
## [1] "The no. of Heads :"
## [1] 30
## [1] "The probability of Heads :"
## [1] 0.6

#one hundredcoin tosses
CoinToss(100)

## [1] "The no. of Tails :"
## [1] 58
## [1] "The probability of Tails :"
## [1] 0.58
## [1] "The no. of Heads :"
## [1] 42
## [1] "The probability of Heads :"
## [1] 0.42

#1 million coin tosses
CoinToss(1000000)

## [1] "The no. of Tails :"
## [1] 499609
## [1] "The probability of Tails :"
## [1] 0.5
## [1] "The no. of Heads :"
## [1] 500391
## [1] "The probability of Heads :"
## [1] 0.5