STA 257 (Fall 2014): Probability and Statistics I

Below is a list of good practice exercises from the text. Do as many as you reasonably can. Bring questions about any of them to the stat aid centre, or for tutorial discussion.

Assignments

• Problem Set 1 (for discussion and quizzing at tutorial Sept 17, but not for hand-in)
  Read Lecture 1 and sections 1.1-1.4 from the textbook.
  Practice problems: p. 26 - 30, # 1, 2, 4, 5, 11, 15, 20, 21, 27, 29, 36, 38, 41, 42.

• Problem Set 2 (for discussion and quizzing at tutorial Sept 24)
  Read Lecture 2 and sections 1.5-1.7 from the textbook.
  Practice problems: p. 27-33, # 7, 47, 49, 50, 56, 62, 69, 71, 77.
  
  Extra problem: If A is an event then the indicator function (rv) of A is defined as I(A)(x)=1 if x is in A and I(A)(x)=0 if x is not in A. I(A) is an example of a discrete rv. It is also called a Bernoulli random variable. Show that I(AUB)=I(A)+I(B)-I(AB) (AB = intersection of A and B).

• Problem Set 3 (for discussion and quizzing at tutorial Oct 1)
  Read Lectures 3 and section 2.1 from the textbook.
  Practice problems: p. 64-67, # 1, 2(b), 3, 4, 6, 7, 11, 12, 19, 25, 31.

• Problem Set 4 (for discussion and quizzing at tutorial Oct 8)
  Read Lectures 4 and sections 2.2 and 4.1 (up to page 119) from the textbook.
  Practice problems: p. 67-69, # 33, 35, 39, 40, 45, 46, 48, 49, 52, 53.

• Problem Set 5 (for discussion and quizzing at tutorial Oct 15)
  Finish lecture 4 and read Lecture 5 and sections 2.3, 4.1 (up to page 123), and 4.2 (up to page 133) from the textbook.
  Practice problems: p. 69 # 57, 58, 62, 67 (a)(b), 68 p. 166 - 169 # 2, 3, 5, 7, 14, 16, 30, 31, 34
  

• Problem Set 6 (for discussion during the TAs' office hours and tutorials Oct 22/Oct29. Note: There are no quizzes on Oct 22 nor Oct 29).
  Read lecture 6 and prepare for the test by doing the following practice questions:
  
  • Practice questions pdf
    Solutions to practice questions pdf
  • Past midterm test pdf and solution pdf.
    For the test, please try to solve it on your own first and then refer to the solution.
  
  
• Problem Set 7 (for discussion and quizzing at tutorial Nov 5)
  Read Lecture 7 and sections 3.1 - 3.3 (up to page 77), 3.4 - 3.5 (up to page 91) from the textbook.
  Practice problems: p. 107-110 # 1, 2, 3, 7, 8, 9, 12, 14, 20, 27.
  
  
• Problem Set 8 (for discussion and quizzing at tutorial Nov 12)
  Read Lecture 8 and sections 4.3 - 4.4, 5.1 - 5.2 from the textbook.
  Practice problems: p. 169-173 # 43, 44, 47, 50, 55, 56, 57, 59, 63, 70, 75; p. 188 # 1, 2.
  
  
• Problem Set 9 (for discussion and quizzing at tutorial Nov 19)
  Read Lecture 9 and sections 3.6, 6.1 - 6.2 from the textbook.
  Practice problems: p. 112-113 #43, 46, 48, 50, 51, 52 (assume both r.v.'s are uniform (0,1)), 61, 63, 64; p. 198 # 5, 6, 7, 8.
  
  
• Problem Set 10 (for discussion and quizzing at tutorial Nov 26)
  Read Lecture 10 and sections 3.7, 4.5 (up to page 160) from the textbook.
  Practice problems: p. 114 # 69, 79; p. 173-174 # 79, 80, 85, 88, 89, 91.
  Useful formula for the joint density function of order statistics (you don't need to derive it) is here: pdf
  
  
• Problem Set 11 (there is no tutorial for that week, please use TAs' office hours to discuss the problems)
  Read Lecture 11 and section 5.3 from the textbook.
  Practice problems: p. 188-190 # 3, 4, 5, 6, 10, 16, 18.
  
  
  
• Some Practice Questions for the Final Exam
  Test 1, Solutions .
  Test 2, Solutions .
  Practice Questions 1.
  Practice Questions 2.

sta257 (Fall 2014): Probability and Statistics I || http://www.utstat.toronto.edu/~olgac/sta257_2014/