Probability 1 (MATH11300), Autumn 2015

Márton Balázs
Tel:+44 (0)117 928-7991
Office:Maths bld. 3.7
Drop in Sessions: Tuesdays 13:00 - 14:00 in teaching weeks, Maths bld. 3.7
except for the 17th of November, which is cancelled.
Q&A Session: 10:00am, 8 January, SM2. Bring your own questions.

  • The official unit description, including assessment methods, texts, syllabus, etc.
  • Mathematics is best learned via examples. It is extremely important that you attend lectures, problem classes and tutorials, solve and hand in homework problems on your own.
  • The lecture slides in pdf. They have gaps, come to lectures. Lectures are recorded but blackboard is not captured. (Last modified: 16 Dec. 2015.)
  • Slides helping the problem class in pdf. Most of problem class material is not featured here and will be on the blackboard instead! Come to problem classes. (Last modified: 7 Oct. 2015.)
  • Homework given out on Weeks 5 and 9 will be assessed and counts 10% towards the final mark.
  • The standard normal distribution in pdf. You will be given a similar table on the exam.
  • The recommended text is: Probability 1 (compiled from the first 8 chapters of "A First Course in Probability" by S. Ross), Pearson Custom Publishing. Alternatively, the Library has copies of A First Course in Probability by S. Ross. These are identical for the parts we need, and have plenty of practice problems, should you find the problem sheets too restricted.
  • You can find additional material here. Except for the lecture slides (similar to those we'll use this year), nothing from there is needed for this unit, nothing will be assessed, nothing is to be handed in. It's simply there for those interested or for further reference once you need to engage a bit more in basic probability. There are nice and interesting problems, and additional material beyond the scope of this unit. I'm happy to discuss about any of that stuff on my office hours.
  • Here is a mock exam. This exam is intended for you to see the style of questions on the exam. Please notice that
    • No two exams are of the same difficulty, the real thing could be easier or more difficult for some.
    • Solving this mock exam does not, in any sense, give you a full preparation for the exam. This is a random selection of some material from the unit, as well as the real exam is. But mind independence.
    • It is probably a good idea to solve it under exam-like circumstances (only statistical tables allowed, 90 minutes time). Once you solved it, you could check your answers with its solutions, available on Blackboard.

Below is a detailed schedule. Topics of future events are plans, and can change. Topics of past events serve as log.
Problem sheets will be available as the teaching block proceeds, with links in the last column. They include mandatory homework, deadlines to be found in the pdf.
Solutions will be available on Blackboard once the due date is passed.

Day Topics Problem sheet
Tue 29 Sep, 12:00 1. Elementary Combinatorics Sheet 1
Thu 1 Oct, 9:00 1. Sample space, axioms of probability
Thu 1 Oct, 12:00 Problem class
Tue 6 Oct, 12:00 1. Simple properties of probability Sheet 2
Thu 8 Oct, 9:00 1. Equally likely outcomes
Thu 8 Oct, 12:00 Problem class
Tue 13 Oct, 12:00 1. Equally likely outcomes, 2. Conditional probability Sheet 3
Thu 15 Oct, 9:00 2. Law of Total Probability, Bayes Thm, independence
Thu 15 Oct, 12:00 Problem class
Tue 20 Oct, 12:00 2. Law of Total Probability, Bayes Thm Sheet 4
Thu 22 Oct, 9:00 2. Independence, conditional independence
Thu 22 Oct, 12:00 Problem class
Tue 27 Oct, 12:00 3. Discrete random variables, mass fct Sheet 5
Thu 29 Oct, 9:00 3. Expectation, variance assessed HW 1
Thu 29 Oct, 12:00 Problem class cover sheet
Tue 3 Nov, 12:00 3. Bernoulli, Binomial Poisson random variables Sheet 6
Thu 5 Nov, 9:00 3. Geometric; Continuous random variables
Thu 5 Nov, 12:00 Problem class
Tue 10 Nov, 12:00 4. Continuous random variables Sheet 7
Thu 12 Nov, 9:00 4. Uniform, Exponential random variables
Thu 12 Nov, 12:00 Problem class
Tue 17 Nov, 12:00 4. Normal, DeMoivre-Laplace CLT, transformations of distributions Sheet 8
Thu 19 Nov, 9:00 5. Joint and conditional distributions, independent variables
Thu 19 Nov, 12:00 Problem class
Tue 24 Nov, 12:00 5. Discrete convolutions, Gamma distribution Sheet 9
Thu 26 Nov, 9:00 6. Properties of expectations. Variance, covariance assessed HW 2
Thu 26 Nov, 12:00 Problem class cover sheet
Tue 1 Dec, 12:00 6. Variance, covariance, correlation Sheet 10
Thu 3 Dec, 9:00 6. Conditional expectation
Thu 3 Dec, 12:00 Problem class
Tue 8 Dec, 12:00 6. Moment generating fcts, 7. Markov's, Chebyshev's ineq Sheet 11
Thu 10 Dec, 9:00 7. Weak Law of Large Numbers, CLT
Thu 10 Dec, 12:00 Problem class
Tue 15 Dec, 12:00 Review
Thu 17 Dec, 9:00 Review
Thu 17 Dec, 12:00 Problem class



If you have any questions, please contact me (see on top). Below is my schedule.



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