The length of time that a 4 gigabyte \(\mathrm{PC}\) computer memory module operates until failure is the outcome of an exponential random variable with mean \(\mathrm{E} X=3.25\), where \(x\) is measured in 100,000 hour units.

(a) Simulate the operating lives of 10 memory modules using the following 10 outcomes from a Uniform \((0,1)\) computer random number generator:

(.2558,.5938,.1424,.9476,.5748,.8641,.0968, \(.5839, .3201, .1577)\).

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