Introduction to Probability and Statistics (18.05) - Spring 2008

Lecturer: Dan Gutfreund
Office: 2-334
E-mail: danny@math.mit.edu
Office hours: Wed. 11-12 or by appointment (via e-mail).

Teaching Assistant: Yulan Qing
E-mail: yulanq@mit.edu
Office: 2-229
Office hours: Thu. 4-5pm or by appointment (via e-mail).

Classes: MWF 10-11
Classroom: 2-139
Textbook: F.M. Dekking, C. Kraaikamp, H.P. Lopuhaa, and L.E. Meester, "A Modern Introduction to Probability and Statistics. Understanding Why and How", Springer, 2005, 488 p.
Prerequisites: 18.01

Description:

Elementary introduction to probability and statistics with applications. Topics covered include probability spaces, discrete and continuous random variables, distribution functions, conditional probability, Bayes' rule, expectation, variance, Markov and Chebyshev inequalities, Law of Large Numbers, Central Limit Theorem, statistical estimation and testing, Confidence intervals, introduction to linear regression.

Announcements:

Problem sets:

General guidelines: Problem sets will be published here (almost) every Friday. Unless stated otherwise, they are to be returned on the following Friday by 12 (noon). You can either hand them in class or drop them in a designated box in the undergraduate office (2-108).
All your solutions must include explanations, even if the final answer is just a number.

Collaboration policy: You are allowed and even encouraged to discuss ways to solve the problem sets with other students. However, each student must fully understand the solutions and write them on his/her own.

  • Problem set 1 (Due Friday Feb. 22nd). Solutions.
  • Problem set 2 (Due Friday Feb. 29th). Solutions.
  • Problem set 3 (Due Friday March 7th). Solutions.
  • Problem set 4 (Due Friday March 21st). Solutions.
  • Problem set 5 (Due Friday April 4th). Solutions.
  • Problem set 6 (Due Friday April 11th). Solutions.
  • Problem set 7 (Due Friday April 25th). Solutions.
  • Problem set 8 (Due Friday May 2nd). Solutions.
  • Problem set 9 (Due Monday May 12th). Solutions.

    • Exams:

    Three in class one-hour tests on March 12, April 16 and May 9.
    There is no final exam.
    Test 1 and its solution.
    Test 2 and its solution.
    Test 3 and its solution.

    Grades:

    Problem sets = 25%, each exam = 25%

    Lectures:

  • Wed. 2/6 - Introduction, sample space, events (Chapter 2).
  • Fri. 2/8 - Probability functions, simple probabilistic identities (Chap. 2).
  • Mon. 2/11 - Uniform probability, counting. Conditional probability (Chap. 3). Lecture notes 1 2 and some additional explanations.
  • Wed. 2/13 - The multiplication rule, the law of total probability (Chap. 3). Lecture notes 1 2 3 4
  • Fri. 2/15 - Bayes' rule, independence of events (Chap. 3). Lecture notes
  • Mon. 2/18 - President's day - no class (the class will be given on Tuesday instead).
  • Tue. 2/19 - Independence of events (Chap. 3), discrete random variables (chap. 4). Lecture notes
  • Wed. 2/20 - Bernoulli, Binomial, Geometric distributions (chap. 4). Lecture notes
  • Fri. 2/22 - Continuous random variables, the uniform distribution (chap. 5). Lecture notes 1 2 3 and some additional explanations.
  • Mon. 2/25 - Exponential and Normal distributions (chap. 5). Lecture notes 1 2
  • Wed. 2/27 - Normal distribution - cont. (chap. 5), expectation (Chap. 7). Lecture notes 1 2
  • Fri. 2/29 - Expectation and variance (Chap. 7). Lecture notes
  • Mon. 3/3 - Variance - cont. (Chap. 7). Joint distributions of discrete r.v.'s (Chap. 9). Lecture notes
  • Wed. 3/5 - Joint distributions of continuous r.v.'s, independent r.v.'s (Chap. 9). Lecture notes
  • Fri. 3/7 - Linearity of expectation (Chap. 10). Lecture notes 1 2 3
  • Mon. 3/10 - Covariance and correlation (Chap. 10). Review before the test. Lecture notes.
  • Wed. 3/12 - Test.
  • Fri. 3/14 - Covariance - cont. (Chap. 10). Sums of independent random variables (Chap. 11). Lecture notes
  • Mon. 3/17 - Markov and Chebyshev's inequalities. The law of large numbers (Chap. 13). Lecture notes 1 2
  • Wed. 3/19 - Using Chebyshev's inequality (Chap. 13). Chernoff bounds. Lecture notes.
  • Fri. 3/21 - The central limit theorem (Chap. 14). Lecture notes.
  • Mon. 3/31 - Graphical representations of datasets (Chap. 15). Lecture notes.
  • Wed. 4/2 - Numerical summaries of datasets (Chap. 16). Basic statistical models (Chap. 17). Lecture notes 1 2
  • Fri. 4/4 - Statistical models (Chap. 17). The bootstrap principle (Chap. 18). Lecture notes 1 2
  • Mon. 4/7 - Unbiased estimators (Chap. 19). Lecture notes.
  • Wed. 4/9 - Biased and Unbiased estimators (Chap. 19), Jensen's inequality (Chap. 8 & 19), Efficiency of estimators (Chap. 20). Lecture notes.
  • Fri. 4/11 - Efficiency of estimators and mean squared error (Chap. 20). Maximum likelihood (Chap. 21). Lecture notes.
  • Mon. 4/14 - Maximum likelihood (Chap. 21). Review before test. Lecture notes.
  • Wed. 4/16 - Test.
  • Fri. 4/18 - Maximum likelihood - cont. (Chap. 21). Lecture notes.
  • Mon. 4/21 - Patriots day - no class.
  • Wed. 4/23 - Linear regression and least squares estimates (Chap. 22). Lecture notes 1 2 3 4 5
  • Fri. 4/25 - Confidence intervals (Chap. 23). Lecture notes 1 2 3
  • Mon. 4/28 - Confidence intervals - cont. (Chap. 23 & 24). Lecture notes 1 2 3
  • Wed. 4/30 - Confidence intervals - cont. (Chap. 24). Lecture notes 1 2 3 4 5
  • Fri. 5/2 - Testing hypotheses (Chap. 25 & 26). Lecture notes 1 2 3 4
  • Mon. 5/5 - Testing hypotheses - cont. (Chap. 25 & 26). The t-test (Chap. 27). Lecture notes.
  • Wed. 5/7 - The t-test for linear regression (Chap. 27). Review before test. Lecture notes 1 2 3
  • Fri. 5/9 - Test (in 3-270).