lego man

gistfile1.r

legoSim <- function() {
  i = 1
	legos <- c()
	while(TRUE) {
		x <- sample(1:16, 1)
		if (x %in% legos == FALSE) {
			legos <- c(legos, x)
			if (length(legos) == 16) { break }
		}
		else { i <- i + 1 }
	}
	return(i)
}

makeCDF <- function(lst) {
	out = c(lst[1])
	z = 2
	s = out[1]
	while(z < length(lst)) { 
		out[z] <- lst[z] + s
		s <- out[z]
		z <- z + 1
	}
	return(out)
}

x   <- replicate(5000, legoSim())
h   <- hist(x, prob=TRUE, breaks=seq(1, 199, by=1))
cdf <- makeCDF(h$density)

plot(cdf, 
     type='l', 
     main='lego man empirical CDF', 
     ylab='P(X <= k)', 
     xlab='k = number of flips',
     xaxt='n',
     col='blue'
)

lbls <- seq(1, length(cdf), by=1)
axis(1, labels=seq(1,199,by=5), at=seq(1,199,by=5))

segments(1, .4916, 34, .4916, col='red', lty=2)
segments(34, .4916, 34, 0, col='red', lty=2)