STAT {3401, 4412}, Introduction to Probability Theory, Spring 2005

Monday
Wednesday

Covered:
Relative frequency histogram; mean, variance and standard deviation; normal distribution; empirical rule;
Basic set notations; sample space

Prepare for calculus quiz.
Install R. (optional)

HW #1: In Chapter 1, do exercises #5, 7, 21. In Chapter 2, do Exercises #1, 5 (Section 2.3).
Due Monday (4/4)

Please UPDATE your blackboard email address! I send out announcements via email from time to time

Solutions to HW posted outside my office

Calculus quiz on Wednesday

The R Project for Statistical Computing (http://www.r-project.org/)

In R, try running the following:
hist(rnorm(100))
?hist
demo(graphics)
hist(faithful[[1]])
hist(faithful[[2]])
?faithful
?q
q()

Covered:
axioms of probability; sample point method;birthday problem; permutation; combination; binomial coefficient;

HW #2: In Chapter 2, do Exercises 11, 13, 15 (Section 2.4); 23 (Section 2.5).; 27, 28, 33, 34, 35, 36, 40, 41, 42, 45, 47, 53, (Section 2.6)
* Due Monday (4/11)
* 2.53 is for 4412 students only

Waitlisted students: Please check if you're in on or after Thursday (4/7). If you're not in even if you signed the addition sheet, please see me next Monday (4/11)

Solutions to HW posted outside my office

In R, try choose(n,r) and factorial(r) function to compute nCr and r!.

For the birthday problem, run: prod(346:365)/365^20

Covered:
Conditional probability; independence; two laws of probability;

HW #3: In Chapter 2, do exercises 59, 60, 65 (Section 2.7); 69, 71, 73, 74, 78, 79 (Section 2.8); 86, 87, 88 (Section 2.9);
* Due Monday (4/18)

Quiz on Coming Monday (4/18/2005)

Covered:
law of total probability and Bayes' rule; random variable; expected value; bionmial;

HW #4: In Chapter 2, 98, 99 (Section 2.10); do exercises 117 (Section 2.11) In Chapter 3, do exercises 1, 4, 7, 9 (Section 3.2);
* Due Monday (4/25)

[everything below this line (grey characters) is tentative]

Covered: geometric; negative binomial

HW #5: 10, 17, 19, 24 (Section 3.3);
In Chapter 3, do 27, 29, 33, 35, 40, 41, 44, 47, (Section 3.4) In Chapter 3, do exercises 50, 51, 55, 63, 72, 74, 75, 79,
Doing these HW enhances preparation for the midterm
* Due Monday (5/2)

Covered: hypergeometric; poisson

Wednesday (5/4) is the Midterm
" Although the exams will be "closed-book", you will be allowed to prepare and use one 8.5" x 11" sheet of notes (on both sides). These notes must be written by hand and may not be composed of photocopies or other machine reproductions of the textbook or of handouts of homework solutions. Also bring your student ID, your own paper (8.5" x 11") and a hand calculator for use during midterm and final exams.

The midterm will be given on May 4, 2005 (Wednesday).

Midterm and solution (PDF)

Here's the distribution of scores of the class.
Min. 1st Qu. Median Mean 3rd Qu. Max.
34.00 65.50 87.00 82.03 97.00 118.00

Covered: Continuous RV; uniform;

HW #6: In Chapter 3, do exercises 84, 85, 91, 97, 98, , 100, 103, 111,
In Chapter 4, do exercises 1,2,3,4, 5, 8, 9, 11,
14, 15, 17, 18, 21, 27,
28, 31, 37, 41, 44,
* Due Monday (5/16)

Covered: normal; gamma; beta; Chebychev

HW #7 In Chapter 4, do exercises
46, 47, 49, 52, 53, 59, 61, 65, 66
67, 68, 69, 73, 77, 81, 84, 85
91, 92, 93, 95, 99,
115, 117, 119 (+ 72), 122, (Chebychev)

* Due Monday (5/23); No need to turn in

Covered: joint, marginal, conditional pdf;

HW #7: In Chapter 5, do exercises 1, 2, 3, 4, 17, 18, 19, 20, 39, 41, 42, 62, 63, 75, 76, 86, 87, 88
* Due Wednesday (5/23); No need to turn it in. Solutions are posted outside my office already.

Quiz 2 and solution (pdf)

Covered: multinomial? MGF?

R code : 3401_final.R

Final project:
- In the code, there are five sets of curves corresponding to normal, gamma, chi-squared, exponential, and beta distribution, each marked by 'xxx'.
- Plot each set of curves.
- Label individual curves in each set by hand (or by computer if you figure out how)
- For each of of the five sets, add one more curve corresponding to the same distribution but with different parameter(s). Label the new curve as well.
- Print out all five sets, each with an additional curve. Label all curves in all the five sets.
- Bring them to the final. Don't forget to write your name on the first page.

Final is on Monday (5/6), 4:00 pm to 5:50 pm.

Final schedule

"Although the exams will be "closed-book", you will be allowed to prepare and use one 8.5" x 11" sheet of notes (on both sides). These notes must be written by hand and may not be composed of photocopies or other machine reproductions of the textbook or of handouts of homework solutions. Also bring your student ID, your own paper (8.5" x 11") and a hand calculator for use during midterm and final exams.