### Paul Johnson
### April 9, 2009
###Andi Nye sent me a starter function that I fixed up.


### Basic idea:
unifMean <- function(n) {
  plot(0, 0, type = "n", xlim = c(0,1), ylim = c(0,13.5),
       xlab = "Density", ylab = "f(x)")
  res = c()
  m = 500; a = 0; b = 1
  for(i in 1:m) res[i] = mean(runif(n, a, b))
  lines(density(res), lwd = 2)
}



unifMean(10)

unifMean(100)

unifMean(1000)




### Maybe I like this better
### Small function to get m means of n observations each

unifMean <- function(n=100, m=100, a=0, b=1) {
  res <- replicate(m,  mean(runif(n, a, b)))
}


x1 <- unifMean()
x2 <- unifMean(100, 50, 0, 1)

  
plot(0, 0, type = "n", xlim = c(0,1), ylim = c(0,13.5),
      xlab = "Density", ylab = "f(x)")

lines(density(x2), lwd = 2)

hist(x2, xlim=c(0,1),breaks=20, prob=T)
lines(density(x2), lwd = 2)


### Same as

plot(density(x2))



Nvalues <- c(5, 10, 50, 100, 500, 1000, 10000)

myUs <- sapply(Nvalues, function(x) unifMean(n=x) )


plot(0, 0, type = "n", xlim = c(0,1), ylim = c(0,13.5),
      xlab = "Density", ylab = "f(x)")

lines(density(myUs[,1]),lty=1)
lines(density(myUs[,2]),lty=2)
lines(density(myUs[,3]),lty=3)
lines(density(myUs[,4]),lty=4)
lines(density(myUs[,5]),lty=5)
lines(density(myUs[,6]),lty=6)




### Also works to get a list of outcomes
myUs <- lapply(Nvalues, function(x) unifMean(n=x) )


plot(0, 0, type = "n", xlim = c(0,1), ylim = c(0,13.5),
      xlab = "Density", ylab = "f(x)")

lines(density(myUs[[1]]))
lines(density(myUs[[2]]))

plot(density(myUs[[1]]))



lapply( myUs, function(x) lines(density(x)))



plot(0, 0, type = "n", xlim = c(0,1), ylim = c(0,13.5),
      xlab = "Density", ylab = "f(x)")


lapply( myUs, function(x) lines(density(x)))



mydensities <- sapply( myUs, function(x) density(x))