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. 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.
Given a joint probability density function, find the marginal distributions for X and Y
What is the expected value of X?
What is the expected value of 3X+2
What is E[X|Y=1]?
What is Cov(X, Y)?