Question

Baseball caps are to be manufactured in one range of sizes for both men and women. Let H be a random variable that measures the head circumference (around the head and right above the eyebrows) for a random individual. Hat manufacturers know that the head circumference for men follows a Gamma distribution with α = 2, β = 4, that the head circumference for women is also Gamma distributed with α = 2, β = 3, and among those who wear baseball caps there are three times as many men as women.

Part 5a: Part 5b: Part 5c:

What is the density function of H? What is the mean of H?

What is the variance of H?

Answer 1