consider the experiment below using population s. we define two discrete random variables, x the numeric value of a randomly drawn circle and the indicator variable y that equals 1 if the selected circle is shaded, and 0 if it is not shaded. a. consider x, the numerical value on the circle. if the circles are equally likely to be chosen (say after shuffling), then in a large number of experiments (i. e., shuffling and drawing one of the ten slips), summarize the probabilities of possible outcomes using a probability density function. b. given a joint probability density function, find the marginal distributions for