Applied Probability (ST2004/ST2352)
a.k.a. Cool Stuff with Random Numbers
Instructor:
E-mail:
Room:
Brett Houlding
[email protected]
Lloyd’s Room 129
Class hours:
Monday
09:00–10:00
ICT Lab 1 & 2
Tuesday
17:00–18:00
LB08
Wednesday
15:00–16:00
LB04
Location of on-line resources:
https://www.scss.tcd.ie/Brett.Houlding/Index/ST2004_ST2352.html
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Assessment
• Exam 2 hours (80%).
• Two compulsory group projects (10% and 10%).
• Reassessment 100% supplimental exam.
• Optional single project worth 30% of your marks and which can only
increase your grade!
• For example, if a standard assessment gives a mark of 40.
• Then if optional project had a mark of 30 the final mark remains at 40.
• But if optional project had a mark of 50 the final mark becomes
0.3 × 50 + 0.7 × 40 = 43.
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What is examinable?
Unless expressly stated otherwise:
• All material presented in class/labs including:
– Material in handouts.
– Anything additional that is written on the blackboard.
– Anything else additional that is said verbally during lectures or labs.
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Reading
• There is one main text, namely Tjims’ ‘Understanding Probability’
(Cambridge 2007).
• Part One is Probability in Action
– Chapter 1 has 12 probability questions.
– Chapters 2 and 3 include detailed case studies.
• Part Two has relevant chapters 7 through 11 and 13.
4
More Reading
• Other texts include:
– Swift, L: ‘Mathematics and Statistics for Business, Management and
Finance’ (MacMillan 1997).
– Dekker, Kraaikamp, Lopuhaa, Meester: ‘A Modern Introduction to
Probability and Statistics’ (Springer 2005).
– Stirzaker, D: ‘Probability and Random Variables: A Beginner’s Guide’
(Cambridge 2005).
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Idea Generating Reads
• Other texts, good for ideas!
– Applebaum, D: ‘Probability and Information’ (Cambridge 2nd edition
2008).
– Plous, S: ‘The Psychology of Judgment and Decision Making’
(Cambridge 2005).
– Taleb, NN: ‘Fooled by Randomness: The Hidden Role of Chance in the
Markets and in Life (Random House, 2005).
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Web Resources
• http://understandinguncertainty.org/
• http://www.rss.org.uk/
• http://www.random.org/
• http://www.intuitor.com/statistics/index.html
• And many others...
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What are we about?
• Making precise statements about uncertainty.
• Uncertainty is lack of information.
– Information means money/competitive advantage.
• Making decisions
– In face of uncertainty!
• Modelling, discussing, evaluating systems.
– Using computer and elementary maths.
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Understanding Uncertainty in ‘Systems’ ?
• Use computers to model uncertainty.
– Using random numbers to represent events.
– Summaries of many replications allow us to consider how a system
with randomness behaves in the long run.
• We will use mathematical notation:
– Precise statements about combining elementary events.
– Probability distributions for random variables.
– Summaries of probability distributions.
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Labs
• We will use Excel in labs.
– Alternative computing platforms fine (I use R in ST2006 and ST3011).
– Pseudo-code ok to use in exam environment.
– If unfamiliar of syntax/functions templates and help are available.
• Excel and Maths:
– Cells such as A1, B3, etc. can represent variables X or Y etc.
– They can contain values, instances, realisations.
– Math formula of Y = 2X 2 + 3 would be represented as an Excel formula
in a particular cell, say B3, of =2*A1^2+3.
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House Rules
• Lectures at 17:00 on Tuesday and 15:00 on Wednesday.
– Tuesday’s we’ll generally try to look at ‘interesting stuff’.
– Wednesday’s we’ll generally look at how to do it.
– Handouts are provided and will go on the course website as material is
presented.
• Formal labs at 09:00 on a Monday for the first 6 weeks.
– I will allow the later weeks for use in projects, and/or office hour.
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Compulsory Projects
• Groups of 3 or 4.
– Self allocation fine, else random allocation by me.
• Dice (10%) due after reading week.
• League Tables (10%) due after term break.
• Two parts:
– Part 1: Conduct specified experiments on a ‘system’ (using computer
generated random numbers).
– Summarise results (hence evaluate the ‘system’ and show that you
understand the use of random numbers).
– Part 2: Investigate ‘something’ in some depth using random numbers.
• 70% of the mark is for ‘getting it right’, 30% is for skill/flair!
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Optional Projects
• Substantial individual project.
• Topic self nominated (in consultation and not directly connected to second
part of compulsory projects).
• Sign up by week 4, submit a draft for feedback by week 10, and submit final
after term break.
• This is worth 30% of your mark (only if of benefit to you).
• Useful for those who struggle in exam environments, or others who wish to
get the higher marks and show their potential which is limited when having
to answer specified questions.
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Timetable
• Weeks 1 through 3: Using random numbers for fun (constructing).
• Weeks 3 through 5: Using random numbers to solve problems (modeling of
uncertain info).
– What is probability of... planning, forecasting, evaluating?
• Weeks 5 through 12: Using random numbers efficiently (mathematics of
uncertain information), and where possible use probability instead!
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Random Numbers in Excel
• RAND() Returns a random number greater than or equal to 0 and less than
1, evenly distributed (changes on recalculation).
– 0.575501, 0.327604, 0.322179 ...
• RANDBETWEEN(-2,+5) returns a random integer between the numbers you
specify.
– 4, -2, 3, ...
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Random Knitting Patterns!
• ‘Download the Excel file for yous size. It uses random numbers to create a
unique pattern every time you open, print, or change it. No row is
dependent on any other row, so it’s fine to start knitting, then re-open the
file and continue under the new version’
• knitty.com/ISSUEsummer08/PATTseatangles.html
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Random Passwords
• ‘Use this password tool to create your new password or as many passwords
as you like!’
• thebitmill.com/tools/password.html
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Random Generators
• Random song lyrics
(http://www.leonatkinson.com/random/index.php/lyrics.html)
– You assent one more davies-like semilens.
• Random Fifty Shades generator (http://www.fiftyshadesgenerator.com/)
– ‘Some girls are happy just to dial the rotary phone when they’re alone,
but I can’t get off without...’
• Random academic paper for computer science
(http://pdos.csail.mit.edu/scigen/) – ‘Introduction: Many end-users would agree that, had it not been for the
Ethernet, the improvement of online algorithms might never have
occurred...’
– Forsooth! Examples have been accepted under peer review
(news.bbc.co.uk/2/hi/americas/4449651.stm)
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Random Generators
• Random Credit Cards (generate.software.informer.com/download-generaterandom-credit-card-numbers/)
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Random Generators
• Random Clouds (http://www.soundspectrum.com/softskies/about.html)
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Random Numbers
• Quantum Random Numbers
comscire.com/cart/index.php?main_page=product_info&cPath=0&products_id=4
• Pseudo random numbers?
• True random numbers (Trinity College: http://www.random.org/)?
• Why? (http://www.rotten.com/library/conspiracy/press-your-luck/)
• https://www.youtube.com/watch?v=nIZRL4IpB4Y
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