A ground-fault-protection circuit breaker is designed to "trip" and interrupt power whenever a ground fault is detected in a power line to which it attached. After it trips, it designed to be able to "reset", and restore power when a reset button is pressed. For a certain brand of circuit breaker, the number of resets that occur to get a reset failure, at which the breaker is no longer functional, can be viewed as the outcome of a geometric probability distribution, Geometric(.1).

(a) Simulate 25 observations on the number of times this brand of circuit breaker is reset, ending in a reset failure.

(b) Calculate the sample mean and variance, and compare them to the true mean and variance.