11/2/2022

Chapter 7 - Continuous Distributions continued - see Chapter 7 - Gamma distributions.pdf

• Gamma Function
• Properties of the gamma function
• Relating the gamma function and the standard normal distribution
• Gamma Distribution
• Properties of the Gamma Distribution
  • Find the k-th non-central moment for the gamma distribution.
  • Use your result for the k-th non-central moment to find the mean and variance of a gamma random variable.
• Moment generating function
• The exponential distribution is a special case of the gamma distribution
• Calculating probabilities, finding percentiles, and generating random observations for normal distributions
  • dgamma(k, shape, scale), pgamma(k, shape, scale), qgamma(k, shape, scale), and rgamma(n, shape, scale) with RStudio
• Example - 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?
• Live coding session with RStudio

We will have a problem session on Friday.