Consider a random sample X1, X2, ..., Xn from a location scale family with density function: f(x, , ) = 1 f x , where and are the location and scale parameters, respectively

a. Show that R1 = S is a pivotal quantity for inference involving , where S 2 is the sample variance. (5 points)

b. Show that X S is a pivotal quantity for inference involving , where X and S 2 are the sample mean and sample variance, respectively. (5 points)