## Probability 1 (MATH11300), Autumn 2014

 Márton Balázs Email: m.balazs@our_city.ac.countrycode Tel: +44 (0)117 928-7991 Office: Maths bld. 3.7 Office hours: Mondays 15:30pm - 16:30pm in teaching weeks, Maths bld. 3.7 except for the 3rd of November, which is cancelled.

 The official unit description, including assessment methods, texts, syllabus, etc.   Mathematics is best learned via examples. It is extremely important that you attend lectures and tutorials, solve and hand in homework problems on your own.   The lecture slides in pdf. They have gaps, come to lectures. (Last modified: 10 Dec. 2014.)   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. This text is available from Blackwell's Bookshop on Park Street. Alternatively, the Library has copies of A First Course in Probability by S. Ross. It has plenty of practice problems, should you find the problem sheets too restricted.   You can find additional material here. Except for the lecture slides (identical to the above ones), 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.   Unit choice supplement for studies in probability and statistics in pdf (and an updated version). This is a document (updated for 15/16) to help unit choices for those planning on serious probability and statistics studies after the first year. As some units build on each other, it is rather important to make the correct choices in time.   Problem sessions, only for those without a tutorial group: Tuesdays, 13:00--13:50, location: Maths SM3.   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, click on the links of 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 30 Sep, 12:00, Phys G42 1. Elementary Combinatorics Sheet 1
Thu 2 Oct, 11:00, Chem LT1 1. Sample space, axioms of probability (sol. avail. on Blackboard)
Tue 7 Oct, 12:00, Phys G42 1. Simple properties of probability Sheet 2
Thu 9 Oct, 11:00, Chem LT1 1. Equally likely outcomes (sol. avail. on Blackboard)
Tue 14 Oct, 12:00, Phys G42 1. Equally likely outcomes Sheet 3
Thu 16 Oct, 11:00, Chem LT1 2. Conditional probability (sol. avail. on Blackboard)
Tue 21 Oct, 12:00, Phys G42 2. Law of Total Probability, Bayes Thm Sheet 4
Thu 23 Oct, 11:00, Chem LT1 2. Independence, conditional independence (sol. avail. on Blackboard)
Tue 28 Oct, 12:00, Phys G42 3. Discrete random variables, mass fct Sheet 5
Thu 30 Oct, 11:00, Chem LT1 3. Expectation, variance (sol. avail. on Blackboard)
Tue 4 Nov, 12:00, Phys G42 3. Bernoulli, Binomial random variables Sheet 6
Thu 6 Nov, 11:00, Chem LT1 3. Poisson, Geometric random variables (sol. avail. on Blackboard)
Tue 11 Nov, 12:00, Phys G42 4. Continuous random variables Sheet 7
Thu 13 Nov, 11:00, Chem LT1 4. Uniform, Exponential random variables (sol. avail. on Blackboard)
Tue 18 Nov, 12:00, Phys G42 4. Normal, DeMoivre-Laplace CLT Sheet 8
Thu 20 Nov, 11:00, Chem LT1 4. Transformations of distributions, 5. Joint and conditional distributions (sol. avail. on Blackboard)
Tue 25 Nov, 12:00, Phys G42 5. Independent variables, discrete convolutions Sheet 9
Thu 27 Nov, 11:00, Chem LT1 5. Gamma distribution (sol. avail. on Blackboard)
Tue 2 Dec, 12:00, Phys G42 6. Properties of expectations Sheet 10
Thu 4 Dec, 11:00, Chem LT1 6. Variance, covariance, correlation (sol. avail. on Blackboard)
Tue 9 Dec, 12:00, Phys G42 6. Conditional expectation Sheet 11
Thu 11 Dec, 11:00, Chem LT1 6. Moment generating fcts (sol. avail. on Blackboard)
Tue 16 Dec, 12:00, Phys G42 7. Markov's, Chebyshev's ineq, Weak Law of Large Numbers Sheet 12
Thu 18 Dec, 11:00, Chem LT1 7. Central Limit Theorem (sol. avail. on Blackboard)