1. Write TRUE or FALSE on your answer sheet for each of the following: (3 pts each) (a) Given the marginal distributions of two random variables X and Y the joint distribution of X and Y can be derived. (b) Given the joint distribution of two random variables X and Y the marginal distributions for both X and Y can be derived. (c) Given the joint distribution of two random variables X and Y the conditional distribution of X given Y can be derived. 2. For each set-up below identify a reasonable distribution (stating any parameters) (1 pts each) (a) A student is required to sell candy bars to raise money for the 6th grade field trip. There are in a very large neighborhood and they are not supposed to return home until five homes buy candy bars. Consider the houses independent with a 0.4 probability of selling a bar. Let X = the number of houses visited until the fifth sale. (b) Let W = the number of ones in 10 rolls of a fair six-sided dice. (c) There are 25 students in class. Eight of the students study statistics and the rest engineering. We sample six students from the class to interview. Define Y = the number of statistics students selected