If a company employees n salespersons, it gross sales in thousands of dollars may be regarded as a random variable having a gamma distribution with alpha=80sqrt(n) and beta=1/2. If the sales cost is $8000 per person, how many salespersons should the company employ to maximize the expected profit?
Identify a continuous probability distribution of interest to you and your partner. Provide the p.d.f, c.d.f, m.g.f, mean, and variance of a R.V. that could be modeled with this distribution. Use the m.g.f. to find verify your derivations of the mean and variance. That is, find the mean and variance again, but this time use the m.g.f.