In simulation studies, the response variable is often a binary (or Bernoulli) variable. Often 1 is used to indicate "success" (or the occurrence of an event) whereas 0 indicates "failure" (or the absence of an event).

For example, the following SAS/IML statements define a vector `x` of zeros and ones:

proc iml; x = {0,1,1,1,0,0,1,1,1,1}; |

If you want to find the proportion of ones in the vector, you could sum up the ones and divide by the length of the vector:

prop = sum(x = 1) / nrow(x); |

However, when you think about it, the logical expression `x=1` is equivalent to `x` itself, because the logical expression is 1 when `x` equals 1 and is otherwise zero. Therefore the proportion of ones in a binary vector is simply `sum(x)/nrow(x)`, which is equivalent to the mean of `x`.
For the example, the proportion of ones (0.7) is the same as the sum of the values (7) divided by the sample size (10), which is the mean.

Consequently, a simpler expression that computes the mean of a binary vector is as follows:

prop = x[:]; /* mean of x */ |

This expression also correctly handles missing values in the `x` vector, whereas the original expression does not.