1. Pasta and rice You are hired by the management of a mtaurant to model its stock probabilis tically. You talk to the oook and he says: We cosh pasta and rice. We always make sure that we have at least 133 lb of pasta or 1015' lb of nice {tf there is at least 133 lb of pasta, for example, we could have no rice at all); the log-ts being that we hate datlp specials and we want to be able to feed a lot of people artth the same dish. However we never have more than 3th? lb of rice or of pasta because we have no space to store it {we are able to store 303 lb of rice and 3th} lb of pasta at the same thne). You decide to model the quantity of pasta as a random Tvariable X and the quantity of rioe as a random variable R. As you have no information beyond what you have heard, so you assume that their joint pdf is constant [within the restrictions that you deduoe from talking to the cook}. a. Draw the joint pdf of X and R. b. Are X and R uncorrelated? Justify your answer. c. Are X and R independent? Justify your