The number of times that a copy machine malfunctions in a day is the outcome of a Poisson process with \(\lambda=.1\).

(a) Simulate the operating behavior of the copy machine regarding the daily number of malfunctions over a 10 day period using the following 10 outcomes from a Uniform \((0,1)\) computer random number generator: \((.5263, .8270, .8509, .1044, .6216, .9214, .1665\), \(.5079, .1715, .1726\) )

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