Consider a random sample X1, X2, ..., X from a location scale family with density function: 1(2,14, 0) = 1-1 (="). f(x, == f where and are the location and scale parameters, respectively a. Show that R = is a pivotal quantity for inference involving , where S2 is the sample variance. b. Show that X is a pivotal quantity for inference involving , where X and S2 are the sample mean and sample variance, respectively.