Statistics and Probability

y Find the transpose of the matrix. 6 7 -7 13 5 19 30 -4 9 0 -2 28 2 State the dual problem for the linear programming problem. Minimize w = 3y1 + 4y2 + 63 + y4 subject to: y1+ 12 + y3+ y4 2 110 By1 + 2y2 + 4y3 + 5y4 2 245 with y1 20, y2 20, y3 20, y4 20 What is the dual problem? V Z= subject to: 13 16 with X1 20, X, 20 Use the simplex method to solve. Minimize w =6y1 + /2 subject to: 4y1 + 4y2 2 16 W 4y1 + 12 221 with y1 20, y2 20 Use A= {4, 5, 7, 8, 9) and B = {2, 6, 8, 9) to find the set An B. 5 Let U = { 15, 16, 17, 18, 19, 20, 21 }, A = { 16, 18, 19, 21 } List the members of each set, using set braces. Let D = {14,17,19), E = {14,16,17,18) and F = (13, 15,16, 17, 19). List the elements in the set (D U E) n F. 7 Shade the Venn Diagram to show the set. (CNE') UD Show that the statement is true by drawing Venn diagrams and shading the regions representing the sets on each side of the equals sign. An (B' UC) = (AnB') U(Anc) A single fair die is rolled. Find the probability of getting a 5. [ A single fair die is tossed. Find the probability of rolling a number greater than 5. A marble is selected at random from a jar containing 3 red marbles, 6 yellow marbles, and 2 green marbles. What is the probability that the marble is red