Law of Large Numbers

Die example

• Expected Value is 3.5

• (1+2+3+4+5+6)/6 = 3.5

• Sooner or later, the mean will be 3.5

library(ggplot2)
library(parallel)

x<-1:1000
y<-simplify2array( mclapply(x,
          function(i)  
            mean(  simplify2array(mclapply(1:i, function(i) sample(1:6,1)))  )
) )

data<-data.frame(x=x, y=y)
plt<-ggplot(data, aes(x,y))+geom_line()
print(plt)

Casino Example

• If toss coin==0, casino wins 10 else casio loses 8

• Expected value for each game is to make 2 unit money

• Sooner or later, casino will make money

library(ggplot2)
library(parallel)
casino=1000
x=c(1:1000)
y=c()

for (i in x){
  
  result<-sample(0:1,1)  
  casinoProfit<-if (result==0) 10 else -8
  casino<-casino+casinoProfit
  y<-c(y, casino)
}



data<-data.frame(x=x, y=y)
plt<-ggplot(data, aes(x,y))+geom_line()
print(plt)