Introduction to Statistics I: Stat 515

Meeting : TuTh 11:15    LGRT 319

Instructor : Luc Rey-Bellet

Office :  1423 J LGRT
Phone :  545-6020
E-Mail :  luc@math.umass.edu
Office Hours :   Tuesday 2:30--3:45,   Thursday 9:30--10:30,   or by appointment.

Text:     Introduction to Mathematical Statistics and Its Applications     by R.J. Larsen and M.L. Marx. Prentice Hall. Third edition 2001.

This course is the first part of the Introduction to Statistics two-courses sequence (Stat 515--516). This first part is, in fact, an introduction to Probability Theory which is the natural language not only of Statistics but also of many other problems in natural sciences and social sciences. Our goals in this class are to introduce the basic concepts of probability theory and to apply them to solve a variety of problems. This class requires a working knowledge of Calculus (in particular series and integrals). Among the subject to be discussed in this class

• 1) The axioms of probability, sample spaces and events.

• 2) Independence and conditional probability. Bayes formula.

• 3) Combinatorics and combinatorial probability.

• 4) Random variables, probability distribution function, cumulative distibution function.

• 5) Special discrete random variables (binomial, Poisson, goemetric).

• 6) Special continuous random variables (uniform, normal, exponential).

• 7) Mean and variance of random variables.

• 8) Jointly distributed random variables, sum of independent random variables

• 9) The law of large numbers and the central limit theorem.

Grade: There will be one midterm exam and one final exam. Homework will be assigned regularly.

• 40% Midterm
• 40% Final Exam
• 20% Homework, attendance and participation

Exams:

• Midterm: October 18, 7:00 pm     Room: LGRT 321

• Final: Tuesday December 20, 8:00 am     Room: LGRCA301

Homework :

Homework #1   (due on Thursday September 15 ):
Section 2.2 : page 23   2.2.2, 2.2.4, 2.2.7;   page 26   2.2.10, 2.2.12, 2.2.15;   page 29   2.2.16, 2.2.17.

Homework #2   (due on Thursday September 22 ):
Section 2.3 : 2.3.1, 2.3.3, 2.3.4, 2.3.5, 2.3.9,
Section 2.4 : 2.4.2, 2.4.4, 2.4.6, 2.4.7, 2.4.10
Section 2.5 : 2.5.1, 2.5.3, 2.5.6, 2.5.8, 2.5.11

Homework #3   (due on Thursday September 29 ):
Section 2.6 : 2.6.2, 2.6.5, 2.6.10, 2.6.14, 2.6.16, 2.6.17, 2.6.21, 2.6.27, 2.6.28, 2.6.33, 2.6.34, 2.6.36

Homework #4   (due on Thursday October 6 ):
Section 2.7  : 2.7.2, 2.7.3, 2.7.10, 2.7.11, 2.7.14, 2.7.16,
Section 2.8  : 2.8.2, 2.8.3, 2.8.4, 2.8.7, 2.8.9, 2.8.10

Homework #5   (due on Thursday October 13 ):
Section 2.9  : 2.9.2, 2.9.4, 2.9.6, 2.9.10, 2.9.18, 2.9.19, 2.9.23, 2.9.25, 2.9.30, 2.9.31, 2.9.37, 2.9.40, 2.9.44, 2.9.48,

Homework #6   (due on Thursday October 20 ):
Section 2.10  : 2.10.1, 2.10.4, 2.10.5, 2.10.9, 2.10.10, 2.10.22
Section 3.2  : 3.2.1, 3.2.5, 3.2.6, 3.2.7, 3.2.9, 3.2.10

Homework #7   (due on Thursday October 27 ):
Section 3.3  : 3.3.1, 3.3.2, 3.3.5, 3.3.7, 3.3.14, 3.3.18, 3.3.21, 3.3.25, 3.3.27
Section 3.4  : 3.4.1, 3.4.2, 3.4.3, 3.4.12, 3.4.16, 3.4.18

Homework #8   (due on Thursday November 3 ):
Section 3.5  : 3.5.1, 3.5.2, 3.5.3, 3.5.5, 3.5.8, 3.5.10, 3.5.25, 3.5.28 (b),(c),(e), 3.5.30, 3.5.32

Homework #9   (due on Thursday November 10 ):
Section 3.6  : 3.6.1, 3.6.4, 3.6.5, 3.6.12, 3.6.13 (a),(b),(c), 3.6.14
Section 3.7  : 3.7.1, 3.7.2, 3.7.3, 3.7.5, 3.7.7, 3.7.10, 3.7.18, 3.7.23, 3.7.24.

Homework #10   (due on Thursday November 17 ):
Section 3.10  : 3.10.1, 3.10.3, 3.10.4, 3.10.7(a),(c), 3.10.12, 3.10.16, 3.10.20, 3.10.22,
Section 3.11  : 3.11.1, 3.11.2, 3.11.3, 3.11.4, 3.11.7, 3.11.9, 3.11.19

Homework #11   (due on Thursday December 1 ):
Section 3.12  : 3.12.1, 3.12.2, 3.12.5, 3.12.7, 3.12.9
Section 3.13  : 3.13.1, 3.13.2, 3.13.3, 3.13.4, 3.13.5, 3.13.8
Section 3.14.  :3.14.1, 3.14.2, 3.14.3, 3.14.4
Homework #12   (due on Thursday December 8 ):
Section 4.2  : 4.2.1, 4.2.2, 4.2.4, 4.2.7, 4.2.16, 4.2.17, 4.2.20, 4.2.25, 4.2.26
Section 4.3  : 4.3.1 (a)(b), 4.3.2 (a)(c)(d), 4.3.5(a)(c), 4.3.7, 4.3.8, 4.3.10, 4.3.15, 4.3.18, 4.3.19, 4.3.22, 4.3.23, 4.3.25, 4.3.26, 4.3.30