Let’s say we wanted to simulate flipping a coin 50 times using the statistical language R, where a 1 is a heads and 0 is tails.

> flips=sample(0:1, 50, replace=T)
> flips [1] 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1
[39] 1 1 1 0 1 0 0 1 1 0 1 1

Now we can plot the values to see which were heads and which were tails:

> plot(flips, main="Coin flips",ylab="0 = tails, 1 = heads")



Raw values of heads and tails

What if we want to see a running total of the number of heads over time? I was faced with just this problem for a completely different domain; I’ve written the function myself multiple times in Java and other languages but I was hoping it would be built-in to a stats language like R.  Fortunately I was right; the command you want is cumsum (cumulative sum).  There are a total of four functions like this:

Cumulative Sums, Products, and Extremes

cumsum(x)
cumprod(x)
cummax(x)
cummin(x)

They work just as you’d expect.

> cumsum(flips)
 [1]  0  1  1  2  2  3  4  5  6  7  8  9 10 10 10 11 12 12 13 14 14 15 15 16 17
[26] 18 19 19 19 20 20 20 20 20 20 21 21 22 23 24 25 25 26 26 26 27 28 28 29 30
> plot(cumsum(flips), main="Number of heads flipped over time",ylab="Number of heads")

Running total of number of heads

This is a trivial example, but it certainly simplifies my life.