Math 5670/6670 (Fall 2008)

 

Instructor:  Dr. Ming Liao, 206 Parker Hall, 844-6568, liaomin@auburn.edu

 

Class time and place:  1:00 pm – 1:50 pm MWF in 248 Parker Hall.

 

Office Hours:  10:50 – 11:30 MWF and 10:20 – 11:30 T, or by appointment

 

Text:  Probability and stochastic processes, by F. Solomon.

 

Tentative Coverage:  1.1 -- 1.4, 2.1 -- 2.4, 3.1 – 3.5, 4.1 -- 4.3, 4.5 – 4.7,

                                5.2 – 5.4, 5.7, 6.1 – 6.4, 8.1 – 8.4, 9.1 – 9.4. 10.1 – 10.6

 

Tests:  There will be 7 tests, each 10 points, based on HW. 

 

Attendance:  5 points added, reduced by 1 for each missed class up to 10 points.

 

Final Exam:  Comprehensive with 30 points.

Wednesday, December 10. 12:00 – 2:30 pm.

 

Grades:  Total 105 possible points.

          Math 5670:   A ³ 85,  B ³ 75,  C ³ 60  and  D ³ 50

          Math 6670:   A ³ 90,  B ³ 80,  C ³ 70  and  D ³ 60

          with possible small adjustment.

 

Test grades:  5670grad.doc

 

Homework and tests schedule:

 

Test Date

Homework

 

1.17, 1.19, 1.23, 2.3, 2.8, 2.15, 2.19, 2.21, 2.23, 2.25.

 

3.1, 3.3, 3.11 – 3.15, 3.20, 3.29, 3.31, 4.2, 4.5, 4.8 – 4.12, 4.26, 4.27, 4.33, 4.35, 4.37.

 

5.1, 5.2 5.3, 5.6, 5.7, 5.8, 5.9, 5.11, 5.17, 5.19. 5.21, 5.23, 5.25, 5.33, 5.34.

 

6.1, 6.5 (use Poisson approximation),

Exercise: Suppose 1 in 1000 lottery tickets is a winning ticket and you bought 500.

(a) Use Poisson distribution to estimate the probability of getting 2 winning tickets.

(b) Use binomial distribution to compute the exact value of this probability.

Also do exercise in Poisson process handout (pp.pdf)

 

8.3, 8.6, 8.9, 8.11, 8.15, 8.17.

 

8.19 (also find density of sum of burn-out time and fix-it time), 9.1, 9.3. 9.9, 9.22 and

Problem 1: Let X be exponential of mean 2 and Y is uniform on (0, 2).  Assume independence.  Find the density of  Z=X+Y.

Problem 2:  Assume  E(X)=2,  Var(X)=4,  E(Y)= -3  and  Var(Y)=5.

(a)  Find  E(2X-3Y+4)  and  E(2X-X2).

(b)  Suppose X and Y are independent.  Find  Var(2X-3Y+4)  and  E(2Y2 -XY).

 

9.33, 9.35.

Problem: Assume E(X) = 2, Var(X) = 4, E(Y ) = -3 and Var(X) = 5.

(a) Assume X and Y are independent.  Let U=2X+3Y and V=4X-Y.  Find r(U,V).

(b) Now suppose X and Y are not independent with r(X,Y)=0.5.  Find r(U,V).

Final Exam

10.2, 10.6, 10.19.  Review sections 3.3, 4.3, 5.2 – 5.5, 6.2, 8.3, 8.4, 9.1 – 9.3.

 

The above information is subject to change.  Follow the instruction given in class.