A nut company markets cans of deluxe mixed nuts containing almonds, cashews, and peanuts. Suppose the net weight of each can is exactly 1 pound, 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 gives all necessary information about the weight of the third type. Let X be the weight of almonds in a selected can and Y be weight of cashews. The joint probability density function for (X,Y) is given by: f(x,y)= (24xy 0≤x≤1, 0≤ysl, x+ys1 otherwise . For any given weight of almonds, find the expected weight of cashews, that is find E(YX=x). Also find V(XIX = x). Problem 1, Part II A diagnostic test for the presence of a disease has two possible outcomes: 1 for disease present and 0 for disease not present. Let X denote the disease state of a patient and let y denote the outcome of the diagnostic test. The joint probability function of X and Y is given by: P(X=0, Y = 0) = 0.8 P(X= 1,Y= 0) = 0.05 P(X= 0,Y= 1) = 0.025 P(X= 1,Y= 1) = 0.125 a. Calculate V(XX=1). b. Find the correlation coefficient between X and Y.