Aparticular brand of dishwasher soap is sold in three sizes: 25 oz, 40 oz, and 65 oz. twenty percent of all purchasers select a 25-oz box, 50% select a 40-oz box, and the remaining 30% choose a 65-oz box. let x1 and x2 denote the package sizes selected by two independently selected purchasers. a. determine the sampling distribution of x, calculate e(x), and compare to m. b. determine the sampling distribution of the sample variance s2 , calculate e(s2 ), and compare to s2 .

Abag contains 3 red marbles, 2 blue marbles, and 2 green marbles. one marble is picked, then another marble. assume that the selections are made with replacement. a) find the probability of picking two red marbles with replacement. b) find the probability of picking a red marble and a blue marble. assume the selections are made without replacement. c) find the probability of picking two red marbles without replacement. d) find the probability of picking a red marble and a blue marble without replacement.