The two-parameter gamma distribution can be generalizedby introducing a third parameter g, called a thresholdor location parameter: replace x in (4.8) by x 2 g andx $ 0 by x $ g. This amounts to shifting the densitycurves in Figure 4.27 so that they begin their ascent ordescent at g rather than 0. The article Bivariate FloodFrequency Analysis with Historical InformationBased on Copulas (J. of Hydrologic Engr., 2013:10181030) employs this distribution to model X 53-day flood volume (108 m3). Suppose that values of theparameters are a 5 12, b 5 7, g 5 40 (very close toestimates in the cited article based on past data).a. What are the mean value and standard deviation of X?b. What is the probability that flood volume is between100 and 150?c. What is the probability that flood volume exceeds itsmean value by more than one standard deviation?d. What is the 95th percentile of the flood volumedistribution?

Chapter 2 Exploring Data with Graphs and Numerical Summaries 2.1 Different Types of Data Categorical Variables: These are variables that you can put into different groups, generally non-numerical answers. Things like favorite colors, political party afﬁliation, or letter grades are categorical variables. Quantitative Variables: These are variables that are represented by numerical values....