2. (a) (4 points) Let X Gamma(,). Use moment generating functions to show that the moment coefficient of skewness of X is 3(X) = 2 . Hint: You can look up the MGF for the gamma distribution in the book. (b) (2 points) Draw graphs of the gamma density for = 0.1, 1, 2, 10, 100 and = 1/. These are five different densities with the same mean and with varying degrees of positive skewness. Label the graph of each density with its skewness. (c) (2 points) Give an example of a density with mean equal to one and neg- ative skewness. How does the graph of this density compare with the posi- tively skewed gamma densities in part (b)? My final point about skewness for this week is that the moment coefficient of skewness of a random observation does not depend on the units of measurement. For example, let C be a temperature measured in degrees celsius, and let F = 59 C + 32 be the equivalent temperature in degrees Fahrenheit. The two random variables C and F have the same skewness