**Instructor: **Eric Slud, Statistics program, Math. Dept.

**Office: ** MTH 2314, x5-5469, email **evs@math.umd.edu**, **Office Hours:** M11, W10,
or by appointment

**Please fill out the on-line Evaluation form on this
Course and instructor, by Tuesday Dec. 10, at http://CourseEvalUM.umd.edu. Thank you.**

** Also please note that I am scheduling a review session for the Final Exam, for anyone who wants it, on the afternoon of Wednesday December 11 4:30-6pm, as an extended office hour in my office at MTH 2314. **

**Course Text:** Sheldon Ross, **
A First Course in Probability**, 10th ed., Pearson.

**Syllabus:** This semester's syllabus, based on the Ross 10th edition.

**Overview:** This course is a solid introduction to the formulation and manipulation of
probability models, leading up to proofs of limit theorems: the law of large numbers and the
central limit theorem. It is a gateway course to serious study of mathematical statistics and
graduate-level applied statistics. Key topics characterizing this course as opposed to more
elementary introductions to Probability include joint distributions and change-of-variable
formulas for them; conditional expectation and its applications; and the formal proofs of limit
theorems.

**Prerequisite: **Math 240-241 or Math 340-341.

**Course requirements and Grading:** there will be graded homework sets (one every 2 weeks,
5 altogether) which together will count 20% of the course grade; (two or three) 15-minute quizzes
in-class that will together count 10%; 2 tests that will count 20% each; and
a final exam that will count 30%.

**Notes and Guidelines.** (a) Homeworks should be handed in as hard-copy in-class, except for
possible occasional due-dates on Fridays when you may submit them electronically, via email,
in pdf format. A percentage deduction (at least 15%) of the overall HW score will generally be made for late papers.

**Homework 1 (due Friday 9/6, 5pm):** Reading is all of Chapter 1 of 10th edition.

**Homework 2 (due Wednesday 9/25, 5pm; 11 problems in all):** Reading consists of Chapters 2, 3
and 4 through 4.8.3.

**also** find
the probability of the event that A is the first to select the red ball and that this happens at A's 3rd pick.]

** Note that we are not assuming anything about any player's winning a game
other than player A. But we are assuming that the events of winning separate games are all (jointly) independent**.

**(I).** Find the probability that a 5-card poker hand from a carefully shuffled deck,

*conditionally given* that it has no red-suit (Heart or
Diamond) cards in it.

**(II).** In terms of the probabilities of three events A, B, C and their 2- or 3-way intersections
(e.g., A∩B, A∩B∩C) give a general expression for the probability that exactly **one** of these
events A, B, or C occurs.

**(III).** A fair die is tossed repeatedly and independently according to the following rules: at the first toss
where a 1, 2 or 4 is seen, the game stops, the number X of the toss is recorded, and the number Y is defined equal
to 2*X if the final toss was a 4, and Y is defined as X/2 if the final toss was a 1 or 2. Find the probability mass
functions for X and Y.

**Homework 3 (due Wednesday 10/23, 5pm; 13 problems in all):** Reading: Chapter 4 Sections 4.9, 4.10,
all of Chapter 5, and Chapter 10 through 10.2.1.

** plus 2 additional problems: (A).** If U is a Uniform(0,1) random variable, find the density function of X = (U+3)

**Homework 4 (due Monday 11/18, 5pm; 12 problems in all):** Reading: Chapter 6, omitting Sections 6.6 and 6.8, and Chapter 7 through Section 7.5.

**Homework 5 (12 problems in all) will be due Monday, December 9, 5pm in class:** Reading:
Chapter 7, Section 7.3 and 7.5 through end, Chapter 8, and Simulation Handout which is the same as the second Handout pdf under handouts **(3)** below.

** 2 Extra problems Sim.1 and Sim.3 ** at end of Simulation Handout.

**(1.)** Practice (i.e., sample) problems for Test 1 on Wednesday, October 9, are posted
here. Tests in this course are closed-book, so you should practice and commit to memory all formulas (or derivations) that you think you will need.

**(2.)** Practice (i.e., sample) problems for Test 2 on Wednesday, November 20, are posted
here. Tests in this course are closed-book, so you should practice and commit to memory all formulas (or derivations) that you think you will need. There is also a linked summary of topics for Test 2.

**(3.)** Here are two handouts here, respectively on Transformation of Random Variables and on Random Number Generation and Simulation. These topics are very
important for concrete illustration of the course material, as they allow us to generate and interpret
`artificial data' to illustrate the meaning of our Probability Limit Theorems (Law of Large Numbers, Central
Limit Theorem). In addition, Simulation gives us an `experimental' avenue to calculate via artificial
data probabilities which may be too difficult to figure analytically.

**(4.)** Here is a handout on Normal
Approximation to Binomial Distribution containing a word-problem worked example, as well as some numerical
examples of the quality of the normal approximation to the Binomial. A graph comparing the distribution function
values of Binom(100,.3) with its approximating normal distribution N(30,21) can be found here.

**(5.)** Here is another handout, on Binomial approximation
to Hypergeometric random variables, and the Poisson approximation to the Binomial. In addition, some simulated-data results are given to show that the expectations and probability mass functions behave as they should according to the relative-frequency interpretation of probabilities.

**First Class: Mon., August 26, 2019****Labor Day, Monday Sept. 2, 2019, NO CLASS****In-class Quiz, first 20 minutes of class, Monday Sept. 23, 2019****Rosh Hashonah (Jewish New Year), Monday Sept. 30, 2019, NO CLASS****First In-class Test, Wednesday October 9****In-class Quiz, first 20 minutes of class, Wednesday Nov. 6, 2019****Second In-class Test, Wednesday November 20****Thanksgiving Break: Nov. 27--31, 2019****Change credit level or drop without W, Sept. 9, 2019****Last schedule-adjustment Date (for Drop/Withdrawal with W): Nov. 4, 2019****Last day of classes: Mon. Dec. 9, 2019****Exam Review, 4:30-6:00pm Wednesday December 11, 2019****Final Examination, in classroom, 4-6pm Sat. Dec. 14, 2019**

**The UMCP Math Department home page.
The University of Maryland home page.
My home page.
© Eric V Slud, December 9, 2019.**