Statistics 100a Homework #1 Solutions

Course: MATH 170A, Probability Theory, Lecture 2, Spring 2017
Prerequisite: Math 32B and Math 33A. Not open to students with credit for Electrical Engineering 131A or Statistics 100A.
Course Content: Probability distributions, random variables and vectors, expectation.
Last update: 14 June 2017

Instructor: Steven Heilman, heilman(@-symbol)ucla.edu
Office Hours: Fridays, 9AM-11AM, MS 5634
Lecture Meeting Time/Location: Monday, Wednesday and Friday, 1PM-150PM, MS 5127
TA: Tianqi Wu, timwu(@-symbol)ucla.edu
TA Office Hours: Thursdays 3PM-5PM, MS 6146
Discussion Session Meeting Time/Location: Tuesday, 1PM-150PM, MS 5127
Required Textbook: D. P. Bertsekas and John N. Tsitsiklis, Introduction to Probability, 2nd edition. (The book is freely available online, though some sections are ordered differently than the textbook.)
Other Textbooks (not required):Elementary Probability for Applications, Durrett. (or a more advanced text for someone who has at least taken 115a and 131a:) Probability: Theory and Examples, Durrett.
First Midterm: Friday, April 28, 1PM-150PM, Broad 2100A
Second Midterm: Monday May 22, 1PM-150PM, MS 5127
Final Exam:Tuesday, June 13, 8AM-11AM, Boelter 2444
Other Resources:Supplemental Problems from the textbook. An introduction to mathematical arguments, Michael Hutchings, An Introduction to Proofs, How to Write Mathematical Arguments
Email Policy:

  • My email address for this course is heilman(@-symbol)ucla.edu
  • It is your responsibility to make sure you are receiving emails from heilman(@-symbol)ucla.edu , and they are not being sent to your spam folder.
  • Do NOT email me with questions that can be answered from the syllabus.
Exam Procedures: Students must bring their UCLA ID cards to the midterms and to the final exam. Phones must be turned off. Cheating on an exam results in a score of zero on that exam. Exams can be regraded at most 15 days after the date of the exam. This policy extends to homeworks as well. All students are expected to be familiar with the UCLA Student Guide to Academic Integrity. If you are an OSD student, I would encourage you to discuss with me ways that I can improve your learning experience; I would also encourage you to contact the OSD office to confirm your exam arrangements at the beginning of the quarter.
Exam Resources: Here are the exams I used when I taught this course in previous quarters: Exam 1Exam 1 SolutionsExam 2Exam 2 Solutions. FinalFinal Solutions. Exam 1Exam 1 SolutionsExam 2Exam 2 Solutions. FinalFinal Solutions. Here is a page containing old exams for another 170A class. Here is a 170A practice midterm (with solutions). Here is a 170A practice second midterm. Here is a 170A practice final. Occasionally these exams will cover slightly different material than this class, or the material will be in a slightly different order, but generally, the concepts should be close if not identical.

Homework Policy:
  • Late homework is not accepted.
  • If you still want to turn in late homework, then the number of minutes late, divided by ten, will be deducted from the score. (The time estimate is not guaranteed to be accurate.)
  • The lowest two homework scores will be dropped. This policy is meant to account for illnesses, emergencies, etc.
  • Do not submit homework via email.
  • There will be 8 homework assignments, assigned weekly on Tuesday and turned in at the beginning of the discussion section on the following Tuesday.
  • A random subset of the homework problems will be graded each week. However, it is strongly recommended that you try to complete the entire homework assignment.
  • You may use whatever resources you want to do the homework, including computers, textbooks, friends, the TA, etc. However, I would discourage any over-reliance on search technology such as Google, since its overuse could degrade your learning experience. By the end of the quarter, you should be able to do the entire homework on your own, without any external help..
  • All homework assignments must be written by you, i.e. you cannot copy someone else's solution verbatim.
  • Homework solutions will be posted on Friday after the homework is turned in.
Grading Policy:
  • The final grade is weighted as the larger of the following two schemes. Scheme 1: homework (15%), the first midterm (20%), the second midterm (25%), and the final (40%). Scheme 2: homework (15%), largest midterm grade (35%), final (50%). The grade for the semester will be curved. However, anyone who exceeds my expectations in the class by showing A-level performance on the exams and homeworks will receive an A for the class.
  • We will use the MyUCLA gradebook.
  • If you cannot attend one of the exams, you must notify me within the first two weeks of the start of the quarter. Later requests for rescheduling will most likely be denied.
  • You must attend the final exam to pass the course.

Tentative Schedule: (This schedule may change slightly during the course.)

Week Monday Tuesday Wednesday Thursday Friday
1Apr 3: 1.1, SetsApr 4: Homework 0 (ungraded)Apr 5: 1.2, Probabilistic ModelsApr 7: 1.2, Probabilistic Models
2Apr 10: 1.3, Conditional ProbabilityApr 11: Homework 1 dueApr 12: 1.3, Conditional ProbabilityApr 14: 1.4, Total Probability Theorem and Bayes' Rule
3Apr 17: 1.5, IndependenceApr 18: Homework 2 dueApr 19: 1.5, IndependenceApr 21: 1.6, Counting
4Apr 24: 2.1, Discrete Random VariablesApr 25: Homework 3 dueApr 26: 2.2, Probability Mass FunctionApr 28: Midterm #1
5May 1: 2.3, Functions of Random VariablesMay 2: Homework 4 dueMay 3: 2.4, Expectation and VarianceMay 5, 2.5, Joint PMFs, Covariance and Variance
6May 8: 2.6, ConditioningMay 9, Homework 5 dueMay 10: 2.6, ConditioningMay 12: 2.7, Independence
7May 15, 2.7, IndependenceMay 16: Homework 6 dueMay 17: 3.1, Continuous random variables and PDFsMay 19: 3.1, Continuous random variables and PDFs
8May 22: Midterm #2May 23: No homework dueMay 24: 3.2, Cumulative Distribution FunctionsMay 26: 3.3, Normal Random Variables
9No classMay 30: Homework 7 dueJun 1: Joint PDFs of Multiple Random VariablesJun 3: 3.5, Conditioning
10Jun 5: 3.5, ConditioningJun 6: Homework 8 due Jun 7: The Continuous Bayes RuleJun 9, Review of Course

Advice on succeeding in a math class:

  • Review the relevant course material before you come to lecture. Consider reviewing course material a week or two before the semester starts.
  • When reading mathematics, use a pencil and paper to sketch the calculations that are performed by the author.
  • Come to class with questions, so you can get more out of the lecture. Also, finish your homework at least two days before it is due, to alleviate deadline stress.
  • Write a rough draft and a separate final draft for your homework. This procedure will help you catch mistakes. Also, consider typesetting your homework. Here is a template .tex file if you want to get started typesetting.
  • If you are having difficulty with the material or a particular homework problem, review Polya's Problem Solving Strategies, and come to office hours.
HomeworkExam SolutionsSupplementary Notes

Хейл высокомерно засмеялся. - Одна из проблем, связанных с приемом на работу самых лучших специалистов, коммандер, состоит в том, что иной раз они оказываются умнее. - Молодой человек, - вскипел Стратмор, - я не знаю, откуда вы черпаете свою информацию, но вы переступили все допустимые границы. Вы сейчас же отпустите мисс Флетчер, или я вызову службу безопасности и засажу вас в тюрьму до конца ваших дней.

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