two.envelopes <- function(){
x <- (rnorm(1))
x <- (abs(as.numeric(format(round(x, 3)))))*10 
#randomly selects a number 
#limits the number of decimal places x can have and muiltples x by 10 to simluate realistic dollar values. 
p <- c(x,2*x)
A <- sample(p, 1, replace=F)
#creates a vector with x and 2x then randomly selects one for A.
if (A == x) {
B <- 2*x
} else {
(B <- x)
}
return(c(A))
}
#sets the value for B based on: if A = x then B = 2x or if A = 2x then B = x
g <- replicate(10000, two.envelopes())


two.envelopes.s <- function(){
x <- (rnorm(1))
x <- (abs(as.numeric(format(round(x, 3)))))*10 
#randomly selects a number 
#limits the number of decimal places x can have and muiltples x by 10 to simluate realistic dollar values. 
p <- c(x,2*x)
A <- sample(p, 1, replace=F)
#creates a vector with x and 2x then randomly selects one for A.
if (A == x) {
B <- 2*x
} else {
(B <- x)
}
return(c(B))
}
#sets the value for B based on: if A = x then B = 2x or if A = 2x then B = x
g.s <- replicate(10000, two.envelopes())

library(ggplot2)
plot(g)
plot(g.s)
ggplot() + aes(g)+ geom_histogram(binwidth=10, colour="black", fill="white")

ggplot() + aes(g.s)+ geom_histogram(binwidth=10, colour="black", fill="white")

ks.test(g, g.s)

#K-S test results

p-value will be approximate in the presence of ties
	Two-sample Kolmogorov-Smirnov test

data:  g and g.s
D = 0.0077, p-value = 0.9283
alternative hypothesis: two-sided

two.envelopes <- function(){
x <- (rnorm(1))
x <- (abs(as.numeric(format(round(x, 3)))))*10 
#randomly selects a number 
#limits the number of decimal places x can have and muiltples x by 10 to simluate realistic dollar values. 
p <- c(x,2*x)
A <- sample(p, 1, replace=F)
#creates a vector with x and 2x then randomly selects one for A.
if (A == x) {
B <- 2*x
} else {
(B <- x)
}
return(c(A,B))
}
#sets the value for B based on: if A = x then B = 2x or if A = 2x then B = x
g <- t(replicate(100, two.envelopes()))
head(g)

#results

      [,1]  [,2]
[1,]  5.23 10.46
[2,]  5.48 10.96
[3,] 25.60 12.80
[4,]  6.17 12.34
[5,]  3.88  7.76
[6,]  7.59 15.18

two.envelopes <- function(){
x <- (runif(1))
x <- (abs(as.numeric(format(round(x, 3)))))*10 
#randomly selects a number 
#limits the number of decimal places x can have and muiltples x by 10 to simluate realistic dollar values.
p <- c(x,2*x)
A <- sample(p, 1, replace=F)
#creates a vector with x and 2x then randomly selects one for A.
if (A == x) {
B <- 2*x
} else {
(B <- x)
}
return(c(A,B))
}
#sets the value for B based on: if A = x then B = 2x or if A = 2x then B = x
g <- t(replicate(100, two.envelopes()))
head(g)

#results

      [,1]  [,2]
[1,] 27.20 13.60
[2,] 28.72 14.36
[3,] 12.49 24.98
[4,] 12.95 25.90
[5,] 61.18 30.59
[6,]  2.66  1.33

two.envelopes<- function(){
x <- (rcauchy(1, location = 0, scale = 1))
x <- (abs(as.numeric(format(round(x, 3)))))*10 
#randomly selects a number 
#limits the number of decimal places x can have and muiltples x by 10 to simluate realistic dollar values. 
p <- c(x,2*x)
A <- sample(p, 1, replace=F)
#creates a vector with x and 2x then randomly selects one for A.
if (A == x) {
B <- 2*x
} else {
(B <- x)
}
return(c(A,B))
}
#sets the value for B based on: if A = x then B = 2x or if A = 2x then B = x
g <- t(replicate(100, two.envelopes()))
head(g)

     [,1]  [,2]
[1,] 10.22 20.44
[2,] 24.54 12.27
[3,]  2.05  4.10
[4,]  8.96  4.48
[5,] 15.44  7.72
[6,] 13.74 27.48

two.envelopes <- function(){
x <- (sample(1:100, 1))
#randomly selects a number 
p <- c(x,2*x)
A <- sample(p, 1, replace=F)
#creates a vector with x and 2x then randomly selects one for A.
if (A == x) {
B <- 2*x
} else {
(B <- x)
}
return(c(A,B))
}
#sets the value for B based on: if A = x then B = 2x or if A = 2x then B = x
g <- t(replicate(100, two.envelopes()))
head(g)

#results

     [,1] [,2]
[1,]   27   54
[2,]  136   68
[3,]   33   66
[4,]   14   28
[5,]   30   60
[6,]   57  114