Consider the supercomputer example from Exercise $5\mathrm{.}20.$ The firm is not sure about some of the relevant costs. The following probability distributions reflect their beliefs about the uncertain costs: the annual operating and maintenance costs are uniformly distributed on the range $[$$$150,000,$ $$250,000]$; the additional operating costs for simulation runs above $15,000$ per year are uniformly distributed on the range $[$$$500,$ $$1500]($per run per year$).$ Use the method of moments to estimate the mean and variance of the costs if the firm purchases the supercomputer and they perform $20,000$ runs per year. Use Monte Carlo sampling to estimate the distribution of costs if the firm purchases the supercomputer and they perform $20,000$ runs per year. Calculate the Mean, $5$th percentile, and $95$th percentile of the distribution. $($Hint: Use the Excel function RandBetween$($Bottom$,$Top$)$ to simulate a uniform distribution$)$