Answer:
Let X be the number of users that do not close Windows properly before someone does including that
person. Then X has a geometric distribution with a success rate of p = 0.9. The expected value of
X is given as 1/p = 1.1111. Define a random variable Y to be the number of users that do not close
windows properly before someone does, not including the final person who closes windows properly. If
X = 1, then Y = 0; if X = 2, then Y = 1; if X = 3, then Y = 2, etc. In general, if X = k, then
Y = k − 1, so we can write Y as a function of X: Y = X − 1. Therefore, E[Y ] = E[X] − 1 = .11111.
The random variable Y has a modified geometric distribution with p = .9.
Explanation:
