A nut company markets cans of deluxe mixed nuts containing almonds, cashews, and peanuts. The net weight of each can is exactly 1 lb, but the weight contribution of each type of nut is random. Because the three weights sum to 1, a joint probability model for any two types of nuts gives all necessary information about the weight of the third type. Let X weight of almonds in any one can and Y weight of cashews in that can. Suppose the joint probability density function is given by f(x,y) = otherwise a) Show that the conditions for a joint probability density function are satisfied b) Find the probability that the two types of nuts make up at most 50% of the total weight. c) Find the marginal probability density function for X. d) Show that fx(x) satisfies the conditions for a probability density function. e) Find the expected value E[X] f) Find the expected value E[XY g) Find the covariance COV[X h) Find the correlation Pxr