Math 5010
Winter Semester 2000
Homeworks

• Homework 1:
  • Pages 17-19, Problems 8, 10, 14, 16, 20, 21, 24
• Homework 2:
  • Pages 54-57, Problems 3, 4, 8, 9, 10, 15, 16, 19
• Homework 3: Reading: Chapters 2 and 3.
  • Page 57, Problem 23 (solve this problem in two ways: by applying conditional prob's as well as using basic counting principles.)
  • Pages 104-105, Problems 1, 4, 6, 8, 11, 12, 14, 16
• Homework 4:
  Reading: Chapter 4. This is an arduous but important homework set; you should understand them all, despite the work involved.
  • Page 105-110, Problems 24, 29, 37, 45 (Conditional Probabilities)
  • Page 110-117, Problems 49, 62, 72 (Independence)
  • Page 173-176, Problems 1, 2, 7, 13, 17, 18, 19 (random variables, pmf.'s, cdf.'s, etc.)
• Homework 5:
  
  • Read Ch. 4; Sections 4.1-4.8 (inclusive)
  • Pages 173-183, Problems 4,5,22,23,26,35,36,38,40,41,70
  • Quiz Preparation: Ch.'s 2,3,4.
• Homework 6:
  
  • Read Ch. 5; 5.1-5.4; skip 5.5.1
  • Midterm preparation: Ch. 1-5; inclusive with the exception of the skipped sections. The remainder of Chapter 5 will not be on the midterm, but will be on the final. The main emphasis is on the material covered by the homeworks (1-6, inclusive), but the problems may be quite different.
  • Page 232, Problems 1,2,3,4 (curve plotting, general properties of pdf's);
  • Page 233, Problem 6 (expectations); solve at least part (a) and at most all parts;
  • Page 235, Problems 21, 22 (standardization of normals and using normal tables)
  • Two problems that are more challenging in nature: pages 236-237, Problems 29 and 35(a).
• Homework 7:
  
  • Quiz #3 on Ch. 5 (no double integrals for this quiz)
  • Consider the function f(x,y) whose value is 2xy, if (x,y) is in the triangle bounded by the three points (0,0), (1,0) and (0,1). Otherwise, f(x,y) =0. Compute the volume under f.
  • Redo the above but replace 2xy by 2(xy+y) everywhere.
• Homework 8:
  
  • No office hour on the week of March 20th. This has been shifted to Monday March 27th, the hour after class.
  • Reading: Ch. 6, Section 1 and for the forthcoming week of March 20th: Section 2
  • Page 293, Problems 1,2,3,4,7 (discrete problems for random vectors)
  • Pages 293-295, Problems 8,9,10,15
• Homework 9:
  
  • Preparation for Quiz 4: Ch. 6, including Jacobians and functions of random vectors
  • Page 295-296, Problems 20,21,22,23,26
  • Page 297-298, Problems 35,36,41,42
  • Page 299-300, Problems 51,52,53,54
• Homework 10:
  
  • Preparation for Quiz 5: Ch. 7, Sections 1, 2, 3, 6
  • Pages 372-376, Problems 1,8, 21
  • Pages 377-378, Problems 29,34,36
  • Pages 383-385, Problem 71,73(b) but omit part (a)
  • Page 387, Theoretical Problem 24
  • Suppose X is a random variables, picked uniformly from [0,2pi], let U = sin(X) and V = cos(X).
    • What is the covariance between U and V?
    • Are U and V independent?
    • (Harder) Find the marginal pdf's of U and V.
• Homework 11: (Used as a study guide; i.e., no quizzes on this.)
  
  • Final preparation; study all of the quizzes, as well as the midterm. (This will be on the final exam sheet.)
  • Page 422-424; Problems 10,11 (consult your lecture notes); 12,13 (consult your lecture notes); 14 (consult your lecture notes); 15