###
###
### file: SamplingDist1.R
###
### estimates sampling distribution discussed in class using a simulation
###
### Instructions for use:
### 1) Copy and paste all the code into an R session (then observe what happens)
### 2) Play around with the parameters to the function to see what happens
### 3) Don't forget to compare the results of your simulation to the theoretical
###    ones derived in class.



simulate.sampling.distribution <- function(n,barplot=TRUE,epdf=TRUE){

  U1 <- runif(n)  # for simulating X1
  U2 <- runif(n)  # for simulating X2
  X1 <- matrix(0,n,1)
  X2 <- matrix(0,n,1)

  X1[U1 <= 0.1] <- 0
  X1[(0.1 < U1) & (U1 <= 0.3)] <- 1
  X1[(0.3 < U1) & (U1 <= 0.7)] <- 2
  X1[U1 > 0.7] <- 3
  
  X2[U2 <= 0.1] <- 0
  X2[(0.1 < U2) & (U2 <= 0.3)] <- 1
  X2[(0.3 < U2) & (U2 <= 0.7)] <- 2
  X2[U2 > 0.7] <- 3

  
  Total =  X1 + X2

  if (barplot){
    barplot(table(Total)/n)
  }
  if (epdf){
    return(table(Total)/n)
  } else {
    return (Total)
  }
  
}

simulate.sampling.distribution(1000)