Chapter 1 Coin Tosses

Modify the program CoinTosses to toss a coin n times and print out after every 100 tosses the proportion of heads minus 1/2. Do these numbers appear to approach 0 as n increases? Modify the program again to print out, every 100 times, both of the following quantities: the proportion of heads minus 1/2, and the number of heads minus half the number of tosses. Do these numbers appear to approach 0 as n increases?

In my simulation 0=Tails and 1=Heads

Expermient Based on 100 Tosses

CoinToss <- sample(0:1,100,rep=T)
cat("Number of Tails Tossed","\n","\n")
## Number of Tails Tossed 
## 
sum(CoinToss==0) #Tails
## [1] 44
cat("\n","Percentage of Tails Tossed","\n","\n")
## 
##  Percentage of Tails Tossed 
## 
sum(CoinToss==0)/100
## [1] 0.44
cat("\n","Number of Heads Tossed","\n","\n")
## 
##  Number of Heads Tossed 
## 
sum(CoinToss==1) #Heads
## [1] 56
cat("\n","Percentage of Heads Tossed","\n","\n")
## 
##  Percentage of Heads Tossed 
## 
sum(CoinToss==1)/100
## [1] 0.56
cat("\n","Number of Heads Minus 1/2","\n","\n")
## 
##  Number of Heads Minus 1/2 
## 
sum(CoinToss==1) - 0.5
## [1] 55.5
CoinToss2 <- sample(0:1,100,rep=T)
cat("Number of Tails Tossed","\n","\n")
## Number of Tails Tossed 
## 
sum(CoinToss2==0) #Tails
## [1] 47
cat("\n","Percentage of Tails Tossed","\n","\n")
## 
##  Percentage of Tails Tossed 
## 
sum(CoinToss2==0)/100
## [1] 0.47
cat("\n","Number of Heads Tossed","\n","\n")
## 
##  Number of Heads Tossed 
## 
sum(CoinToss2==1) #Heads
## [1] 53
cat("\n","Percentage of Heads Tossed","\n","\n")
## 
##  Percentage of Heads Tossed 
## 
sum(CoinToss2==1)/100
## [1] 0.53
cat("\n","Number of Heads Minus 1/2","\n","\n")
## 
##  Number of Heads Minus 1/2 
## 
sum(CoinToss2==1) -0.5
## [1] 52.5
CoinToss3 <- sample(0:1,100,rep=T)
cat("Number of Tails Tossed","\n","\n")
## Number of Tails Tossed 
## 
sum(CoinToss3==0) #Tails
## [1] 49
cat("\n","Percentage of Tails Tossed","\n","\n")
## 
##  Percentage of Tails Tossed 
## 
sum(CoinToss3==0)/100
## [1] 0.49
cat("\n","Number of Heads Tossed","\n","\n")
## 
##  Number of Heads Tossed 
## 
sum(CoinToss3==1) #Heads
## [1] 51
cat("\n","Percentage of Heads Tossed","\n","\n")
## 
##  Percentage of Heads Tossed 
## 
sum(CoinToss3==1)/100
## [1] 0.51
cat("\n","Number of Heads Minus 1/2","\n","\n")
## 
##  Number of Heads Minus 1/2 
## 
sum(CoinToss3==1)-0.5
## [1] 50.5

500 Tosses

CoinToss3 <- sample(0:1,500,rep=T)
cat("Number of Tails Tossed","\n","\n")
## Number of Tails Tossed 
## 
sum(CoinToss3==0) #Tails
## [1] 242
cat("\n","Percentage of Tails Tossed","\n","\n")
## 
##  Percentage of Tails Tossed 
## 
sum(CoinToss3==0)/500
## [1] 0.484
cat("\n","Number of Heads Tossed","\n","\n")
## 
##  Number of Heads Tossed 
## 
sum(CoinToss3==1) #Heads
## [1] 258
cat("\n","Percentage of Heads Tossed","\n","\n")
## 
##  Percentage of Heads Tossed 
## 
sum(CoinToss3==1)/500
## [1] 0.516
cat("\n","Number of Heads Minus Half Number of Tosses","\n","\n")
## 
##  Number of Heads Minus Half Number of Tosses 
## 
sum(CoinToss3==1)-250
## [1] 8

1000 Tosses

CoinToss5 <- sample(0:1,1000,rep=T)
cat("Number of Tails Tossed","\n","\n")
## Number of Tails Tossed 
## 
sum(CoinToss5==0) #Tails
## [1] 465
cat("\n","Percentage of Tails Tossed","\n","\n")
## 
##  Percentage of Tails Tossed 
## 
sum(CoinToss5==0)/1000
## [1] 0.465
cat("\n","Number of Heads Tossed","\n","\n")
## 
##  Number of Heads Tossed 
## 
sum(CoinToss5==1) #Heads
## [1] 535
cat("\n","Percentage of Heads Tossed","\n","\n")
## 
##  Percentage of Heads Tossed 
## 
sum(CoinToss5==1)/1000
## [1] 0.535
cat("\n","Number of Heads Minus Half Number of Tosses","\n","\n")
## 
##  Number of Heads Minus Half Number of Tosses 
## 
sum(CoinToss5==1)-500
## [1] 35