(10%) First a point Y is selected at random from the interval (0, 1). Then another point X is selected at random from the interval (Y, 1). Find the probability density function of X.

Problem 7. (2.5 %) Consider two random variables X and Y, each taking val- ues in {1,2,3}. Let their joint PMF be such that for any 1 ≤ x, y ≤ 3,Then, (i) X and Y can be independent or dependent depending upon the strictly positive values(ii) X and Y are always independent(iii) X and Y can never be independent