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1 = Introduction to Probability with MATLAB, spring 2014 =
2
3 === Lecturer ===
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5 [[Jukka Kohonen>>doc:mathstatHenkilokunta.Kohonen, Jukka]]
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7
8 === Scope ===
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10 5 cr
11
12 === Type ===
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14 This course is aimed for international students with a background in Computer Science or an application discipline, such as Bioinformatics Master´s program (MBI). No background in statistics or probabilistics is required.
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16 The course can be included in advanced studies in the MBI program.
17
18 === Contents ===
19
20 The course starts from the elements of probability calculus, and will cover topics and concepts such as:
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22 * probability, joint probability, and conditional probability
23 * random variable
24 * some elementary distributions such as binomial, uniform, exponential, and normal
25 * probability density function (pdf), cumulative distribution function (cdf)
26 * expected value, variance, and other useful statistics of a distribution
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28 **MATLAB** is used as an educational tool in exercises, to obtain a **practical understanding** of random variables and probability distributions. (This is **not**, however, a course **about** MATLAB programming. The course will cover MATLAB only to such extent as is needed to use it for studying probability. Also, no previous familiarity with MATLAB is needed.)
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30 === Prerequisites ===
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32 Elementary calculus
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34 === Lectures and exercises ===
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36 The course lasts 6 weeks, starting 21.1.2014 and ending 26.2.2014.
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38 Weekly schedule:
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40 * Tue 12-14: lecture in room C128
41 * Tue 14-16: exercises in room C128
42 * Wed 12-14: lecture in room CK111
43 * Wed 14-16: exercises in room C128
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45 The exercise sessions are instructed by Brittany Rose.
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47 There are no deadlines for the exercises since no credits are given for them. Doing the exercises is for learning the topics. However, you **may** return your answers (on paper or in e-mail) if you wish to have comments on them.
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49 === Exercise problems ===
50
51 * [[Exercise set 1>>attach:ex1.pdf]]
52 * [[Exercise set 2>>attach:ex2.pdf]]
53 * [[Exercise set 3>>attach:ex3.pdf]]
54 * [[Exercise set 4>>attach:ex4.pdf]]
55 * [[Exercise set 5>>attach:ex5.pdf]]
56 * [[Exercise set 6>>attach:ex6.pdf]]
57 * [[Exercise set 7>>attach:ex7.pdf]]
58 * [[Exercise set 8>>attach:ex8.pdf]]
59 * [[Exercise set 9>>attach:ex9.pdf]]
60 * [[Exercise set 10>>attach:ex10.pdf]]
61 * [[Exercise set 11>>attach:ex11.pdf]]
62 * Auxiliary MATLAB functions can be found [[here>>url:http://www.helsinki.fi/~~kohonen/introprob/||shape="rect"]].
63 * A Very Quick Guide to MATLAB is [[here>>attach:matlabhelp.pdf]].
64
65 === Lecture topics ===
66
67 * [[Lecture 1>>attach:lecture1.pdf]] (21.1.)
68 * [[Lecture 2>>attach:lecture2.pdf]] (22.1.) (More combinatorics: binomial coefficient, sampling); non-equiprobable finite probability space
69 * Lecture 3 (28.1.): Product rule; conditional probability; Bernoulli trial (= repeated independent experiments with same probability of success each time)
70 * Lecture 4 (29.1.): More about conditional probability; law of total probability; Bayes's rule (inverting the conditional probability)
71 * Lecture 5 (4.2.): Random variable; discrete distribution; binomial and geometric distribution; expected value and median
72 * Lecture 6 (5.2.): Discrete distributions and expected value continued
73 * Lecture 7 (11.2.): Continuous distributions; uniform distribution; density function; empirical histogram
74 * Lecture 8 (12.2.): Continuous distributions continued. Pdf, cdf, expected value. Expected gain from a bet, linked to subjective probability.
75 * Lecture 9 (18.2.): Exponential distribution. Distribution of a sum. [[Multinomial coefficient and multinomial distribution.>>attach:lecture9.pdf]]
76 * Lecture 10 (19.2.): Expected value of a function g(X). Variance and standard deviation.
77 * [[Lecture 11>>attach:lecture11.pdf]] (DRAFT) (25.2.): Markov's and Chebyshev's inequalities, and law of large numbers (G&S: Chapter 8).
78 * [[Lecture 12>>attach:lecture12.pdf]] (26.2.): Normal distribution and the central limit theorem. Distribution of a maximum (of any distribution).
79
80 Lecture slides are provided here if they exist. For blackboard lectures there may not be slides.
81
82 === Extra reading ===
83
84 * There is a nice textbook by Grinstead and Snell available at
85 [[http:~~/~~/www.math.dartmouth.edu/~~~~prob/prob/prob.pdf
86 >>url:http://www.math.dartmouth.edu/~~prob/prob/prob.pdf||shape="rect"]]This intro course will not cover everything in the book, but it provides good reading for deeper understanding.
87 * Important topics include the following:\\
88 ** Chapter 1: Idea of random variable. Section 1.2: definitions and theorems.
89 ** Chapter 2: Continuous randon variable. Density function and cumulative distribution function.
90 ** Chapter 3: "A Counting Technique" = rule of product. Permutations, factorials, combinations, binomial coefficient. Bernoulli trial and binomial distribution. (Card shuffling is out of scope.)
91 ** Chapter 4: Conditional probabilitiy. Definitions and theorems. Bayes' formula. (Joint density, beta density are out of scope.)
92 ** Chapter 5: Discrete uniform, binomial, geometric, hypergeometric distribution; continuous uniform, exponential, normal distribution. (Other distributions are out of scope.)
93 ** Chapter 6: Definition, interpretation and theorems of expected value and variance.
94 ** (Chapter 7 is out of scope.)
95 ** Chapter 8: Chebysev, and law of large numbers.
96 ** Chapter 9: Central limit theorem (what it means and how it is used). Proof of CLT is out of scope.
97 ** (Chapters 10—12 are out of scope.)
98 * "Out of scope" means it did not fit this one-period introductory course (and will not be required in the exam), but for further studies in probability, many of these chapters contain much useful reading.
99
100 === Exams ===
101
102 The course is passed by taking a single **course exam**, which is held at the [[general examination>>url:https://wiki.helsinki.fi/display/mathstat/General+exams||shape="rect"]], **Tuesday 4.3.2014 starting at 12**.
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104 General examinations are arranged at** Exactum A111 and B123. **The detailed information about the place can be found on the exam day from the **note on the door** of the auditorium.
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106 Note: Although the general examination (where many different exams can be taken) lasts four hours, **this course exam lasts 2 hours** (you have to return your answers in two hours).
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108 You can bring the following tools to the exam: a calculator; an A4 sheet of handwritten notes (you can use both sides of the paper); the [[MAOL book of tables>>url:http://www.suomalainen.com/oppikirjat/oppikirjat/maol-taulukot-sku-p9511206079||shape="rect"]]. At the exam we will provide you [[this printed collection of tables>>attach:taulukkoliite.pdf]].
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110 **Update 13.3.2014: The exam has been graded. **The results will be registered to Weboodi soon, and** will appear [[here>>url:https://wiki.helsinki.fi/pages/viewpage.action?pageId=129010105||shape="rect"]]**. For any questions about the grading, contact the lecturer.
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114 === [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57781||shape="rect"]] ===
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116
117 Did you forget to register? [[ What to do?>>doc:mathstatOpiskelu.Kysymys4]]
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119 === ===
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