I. Write A if the statement is correct, B otherwise. (10 pts) 1. A discrete uniform distribution has a mean of NIL. 2. Bernoulli distribution is a binomial distribution with p = 1. 3. In a Binomial Experiment the standard deviation of all values is equal to npq - 4. The Binomial distribution ia symmetric when p = 0.5. 5. The possible values of a Hypergeometric distribution are {1, 2, .. . min (n, K )). 6. In a Poisson distribution , A is the maximum number of outcomes occuring in the given time interval or specified region. 7. When independent Bernoulli trials are repeated , each with probability of success p, the number of trials X it takes to get the first success has a Geometric distribution B. A Negative Binomial distribution represents how long (in terms of number if failures) one waits for the r success 9. The marginal pdfs may be used to compute probabilities that involve only X or Y. 10. A joint CDF is a function with domain t the k dimensional Euclidean space Re and coun - terdomain [0, 1]- II. Solve for the following problems. Show your solutions. (40 pts) 1. An observer stands at an overpass of a highway and counts the cars that pass by. He stopa counting when he sees a red car . The proportion of cars which are red is 0.2 . Let X be the number of cars counted a. What distribution does X follow? (2 pts) b. What is the expected value of X? (3 pts ) c. What is the probability that 10 cars will be observed ? (4 pts ) 2. Suppose that 3 balls are randomly selected from an urn containing 3 red , 4 white , and 5 blue balls. If we let X and Y denote, respectively, the number of red and white balls chosen . Hint : This is an extension of Hypergeometric distribution a. What are the possible values of X and Y? (2 pts ) b. Show the joint pmf of X and Y. (8 pts ) 3. If X and Y have joint pdf given by fx,Y(I, ") = 2 (o, ) (x )(0,1) (3)