Matehematics A4 in English - Probability Theory
2017 Fall
Andras Vetier

Requirements

Interactive Electonical Probability Text Book 

Suggested textbooks in probability


Photo pictures of probability lectures Fall 2017 taken a student - thanks to him

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Excel files we made in class
Students should be able to construct such files:
 
2017-09-11___01_rel_freq.xlsx
2017-09-11___02_sum_of_2_dice.xlsx
2017-09-11___03_abs_value_of_the_difference_of_2_dice.xlsx
2017-09-11___04_max.xlsx
2017-09-11___05_max_of_5_dice.xlsx

2017-09-12___01_fair_die.xlsx
2017-09-12___02_RAND-command.xlsx
2017-09-12___03_RAND-squared-command.xlsx
2017-09-12___04_square-root_of_RAND-command.xlsx

Homework for 18 September:

Learn Chapters 1-5 of
http://math.bme.hu/~vetier/df/Part-I.pdf
Solve problems from Chapters 1-5 of
http://math.bme.hu/~vetier/df/Part-I__PROBLEMS.pdf
On the small test on 18 September (Monday) there will be
   - a theoretical question from Chapters 1-5 of http://math.bme.hu/~vetier/df/Part-I.pdf
   - a problem from Chapters 1-5 of http://math.bme.hu/~vetier/df/Part-I__PROBLEMS.pdf

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Excel files we made in class
Students should be able to construct such files:

2017-09-18___01_prob_calc.xlsx

2017-09-19___01_uniform_on_rectangle.xlsx

2017-09-19___02_NON-uniform_on_rectangle.xlsx
2017-09-19___03_NON-uniform_on_rectangle.xlsx


Excel files we used in class
Students are not expected to construct such files:


2017-09-19___04_Buffon.xls
2017-09-19___05_Buffon_50_Experiments.xls




Homework for 25 September:

Learn Chapter 6 of
http://math.bme.hu/~vetier/df/Part-I.pdf
Solve problems from Chapter 6 of
http://math.bme.hu/~vetier/df/Part-I__PROBLEMS.pdf
On the small test on 25 September (Monday) there will be
   - a theoretical question from Chapter 6 of http://math.bme.hu/~vetier/df/Part-I.pdf
   - a problem from Chapter 6 of http://math.bme.hu/~vetier/df/Part-I__PROBLEMS.pdf

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Excel files we made in class
Students should be able to construct such files:


2017-09-26___01_sick_or_not.xlsx
2017-09-26___02_binom_dist.xlsx

Homework for 2 October:

Learn Chapters 7, 8, 9 of
http://math.bme.hu/~vetier/df/Part-I.pdf
Solve problems from Chapters 7, 8, 9 of
http://math.bme.hu/~vetier/df/Part-I__PROBLEMS.pdf
On the small test on 2 October (Monday) there will be
   - a theoretical question from Chapter 8 or 9 of http://math.bme.hu/~vetier/df/Part-I.pdf
   - a problem from Chapter 8 or 9 of http://math.bme.hu/~vetier/df/Part-I__PROBLEMS.pdf

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Notice:
On the 7th week that is on 16 and 17 October no lessons will be held.
This is why our lessons on the 5th, 6th, 8th, 9th, 10th, 11th weeks will be 15 minutes longer,
they will be 105 minutes long instead of 90 minutes.
The Monday lessons on these 6 week will be from 12:15 to 2:00pm (
105 minutes),
the Tuesday lessons on these 6 week will be from 10:15 to 12:00pm
(105 minutes).
Thank you for your understanding and cooperation.

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Excel files we made in class
Students should be able to construct such files:



2017-10-02___01_rel_freqs_probs_FOR_BINOMIAL_DIST.xlsx

2017-10-02___03_File_Students_Should_Be_Able_To_Construct.xlsx
2017-10-03___02_Hypergeom_dist.xlsx

Homework for 7 October:

Learn what we discussed in the Escel file
2017-10-02___03_File_Students_Should_Be_Able_To_Construct.xlsx
and learn also Chapters 1-4 of
http://math.bme.hu/~vetier/df/Part-II.pdf

Construct a file similar to
2017-10-02___03_File_Students_Should_Be_Able_To_Construct.xlsx
so that you do not use this file at all and
solve problems from Chapters1-4 of
http://math.bme.hu/~vetier/df/Part-II__PROBLEMS.pdf
On the small test on 7 October (Monday) there will be
   - a question related to the file 2017-10-02___03_File_Students_Should_Be_Able_To_Construct.xlsx
   - a problem from Chapters 1-4 of http://math.bme.hu/~vetier/df/Part-II__PROBLEMS.pdf

I think software students would enjoy to contruct a simulation for choosing without replacement.
First make the simulation for choosing only 2.
Then 3, then 4, and so on.

Let us learn each other's language (as regards the Excel commands):
Students who use Excel with a language different from English
are asked to send an email to 
vetier@math.bme.hu   with subject: " Excel with a language different from English",
and then I will send a list of the names of some Excel commands in English and in Hungarian,
and then the students will return the list with the names of Excel commands in their own language (French, German, Spanish, and so on).
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Excel files we used in class
Students are not expected to construct such files:
2017-10-10___01_Neg-binom_Random_Variable_Optimistic__Simulation_with_Bulbs.xls
2017-10-10___02_Neg-binom_Random_Variable_Pessimistic__Simulation_with_Bulbs.xls

Excel files we made in class
Students should be able to construct such files:
2017-10-10___03_Second_order_negative_binom_distr_(optimistic).xlsx
2017-10-10___04_Third_order_negative_binom_distr_(optimistic).xlsx
2017-10-10___05Tenth_order_negative_binom_distr_(optimistic).xlsx
2017-10-10___06_Third_order_negative_binom_distr_(optimistic).xlsx
2017-10-10___07_Neg_bin_dist_Excel_function.xlsx

Homework for 24 October, Tuesday, when we meet the next time :
Learn Chapters 5-9 of
http://math.bme.hu/~vetier/df/Part-II.pdf
Solve problems from  Chapters 5-9 of
http://math.bme.hu/~vetier/df/Part-II__PROBLEMS.pdf
On the small test on 24 October (Tuesday) there will be
   - a question related to negative binomial distribution
   - a question related to Poisson distribution
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Excel files we made in class
Students should be able to construct such files:
2017-10-24___01_Mode_of_binomial_distr.xlsx
2017-10-24___02_Expected_value_of_binomial_distr.xlsx


Homework for 30 October, Monday:
Learn Chapters 14-16 of
http://math.bme.hu/~vetier/df/Part-II.pdf
Solve problems from  Chapters14-16 of
http://math.bme.hu/~vetier/df/Part-II__PROBLEMS.pdf
On the small test on 30 October there will be
   - a question related to the notion of the mode
   - a question related to the notion of the expected value
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Excel files we made in class
Students should be able to construct such files:
2017-10-31___01_UNIFORM_between_0_and_1.xlsx
2017-10-31___02_UNIFORM_between_0_and_5.xlsx
2017-10-31___03_UNIFORM_between_A_and_B.xlsx
2017-10-31___04_UNIFORM_between_A_and_B__graphs_off(x)_and_F(x).xlsx

Homework for 6 November, Monday:
Learn Chapters 1, 2, 4,  6, 7  of
http://math.bme.hu/~vetier/df/Part-III.pdf
Solve problems from  1, 2, 4,  6, 7  of
http://math.bme.hu/~vetier/df/Part-III__PROBLEMS.pdf
On the small test on 6 November there will be
   - a question related to the notion of the density and/or distribution functions (chapters 1, 2, 4)
   - two problems related to uniform distribution (chapters 6, 7)

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Our 45 minute long midterm test will be on 13 October, Monday in our usual classroom.

Material of the test:
    - Chapters 1 - 9 of   http://math.bme.hu/~vetier/df/Part-I.pdf   and   http://math.bme.hu/~vetier/df/Part-I__PROBLEMS.pdf
    - Chapters 1 - 9, 14 - 18 of   http://math.bme.hu/~vetier/df/Part-II.pdf   and   http://math.bme.hu/~vetier/df/Part-II__PROBLEMS.pdf
    - Chapters 1, 2, 4, 6, 7, 11, 13, 16, 17  of   http://math.bme.hu/~vetier/df/Part-III.pdf   and   http://math.bme.hu/~vetier/df/Part-III__PROBLEMS.pdf

There will be
     - a "theoretical" question (students will give the answer by sentences) and
     - a problem (to be solved mathematically with or without Excel)
from each of the 3 Parts. Students may but not have to use Excel.

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Excel files we made in class
Students should be able to construct such files:

2017-11-14___01_standard_deviation_for_a dataset.xlsx
2017-11-14___02_standard_deviation_for_random_variables.xlsx

Homework for 20 November, Monday:
Learn Chapter 19  of
http://math.bme.hu/~vetier/df/Part-III.pdf
Solve problems from Chapter 19  of
http://math.bme.hu/~vetier/df/Part-III__PROBLEMS.pdf
On the small test on 6 November there will be
   - a question related to this chapter
   - a problem related to this chapter

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Excel files we made in class:
2017-11-20___01_2-dim_distribution.xlsx
2017-11-21___01_2-dim_CONT_distribution.xlsx
2017-11-21___02_2-dim_CONT_distribution.xlsx
2017-11-21___03_2-dim_CONT_distribution.xlsx
2017-11-21___04_EXPECTED_VALUE_OF_A_FUNCTION.xlsx

Homework:

      - Learn Chapter 20  of
http://math.bme.hu/~vetier/df/Part-II.pdf
Solve problems from Chapter 19  of
http://math.bme.hu/~vetier/df/Part-II__PROBLEMS.pdf

      - Learn Chapters 1, 2, 4  of
http://math.bme.hu/~vetier/df/Part-IV.pdf
Solve problems from Chapters 1, 2, 4 until "Conditional distribution function"  of
http://math.bme.hu/~vetier/df/Part-IV__PROBLEMS.pdf
You may skip:
     Distriburtion function in two dimensions
     Covariance and covariance matrix
     Correlation cefficient

Using the tables in 2017-11-20___01_2-dim_distribution.xlsx
Find the second moment of X
Find the variance of X
Find the conditional second moments of X on cond that Y is given
Find the conditional standard deviations of X on cond that Y is given
Find the conditional variances of X on cond that Y is given
Find the second moment of Y
Find the variance of Y
Find the conditional second moments of Y on cond that X is given
Find the conditional variances of Y on cond that X is given
Find the conditional standard deviations of Y on cond that X is given

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Extra repeated test: 13 Dec (Wednesday) 10am (instead of 8am) E1B
(Students have to register in Neptun for this test)

Exam for those whose midterm work was good: 13 Dec (Wednesday)
10am (instead of 8am) E1B
(Students who take part at this exam have to register in Neptun for the 18 Dec exam,
and send an email to   vetier@math.bme.hu    with the title  EXTRA EXAM   until  Sunday midnight.)

Regular exams:
18 Dec (Monday) 10am E1B
08 Jan (Monday) 10am E1B
15 Jan (Monday) 10am E1B
22 Jan (Monday) 10am E1B
(Students have to register in Neptun for these exams)

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Photo pictures of probability lectures Fall 2017 taken by a student - thanks to him


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Excel files we used in class:
2017-11-27___01_Height_Weight.xls
2017-11-27___02__HeightWeigh_EigenVect_Proj_CondDist.xls
2017-11-27___03_conditional_probabilites_for_normal_distr.xlsx

Pay a special attention to this table, learn to use it as we did in class:
2017-11-28___01_St_norm_dist_TABLE.xlsx

      - Learn Chapter 5  of
http://math.bme.hu/~vetier/df/Part-IV.pdf
Solve problems from Chapter 5 of
http://math.bme.hu/~vetier/df/Part-IV__PROBLEMS.pdf

Results during the term
including repeated test results
are here:   results.xlsx

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Material for the Extra repated test and for all the exams:

Part-I
1 Introductory problems
2 Outcomes and events
3 Relative frequency and probability
4 Random numbers
5 Classical problems
6 Geometrical problems, uniform distributions
7 Basic properties of probability
8 Conditional relative frequency and conditional probability
9 Independence of events

Part-II
1 Discrete random variables and distributions
2 Uniform distribution (discrete)
3 Hyper-geometrical distribution
4 Binomial distribution
5 Geometrical distribution (pessimistic)
6 Geometrical distribution (optimistic)
9 Poisson-distribution
10 Higher dimensional discrete random variables and distributions 29
13 Generating a random variable with a given discrete distribution 36
14 Mode of a distribution
15 Expected value of discrete distributions
16 Expected values of the most important discrete distributions
17 Expected value of a function of a discrete random variable
18 Moments of a discrete random variable
19 Projections and conditional distributions for discrete distributions
20 Transformation of discrete distributions

Part-III
1 Continuous random variables
2 Distribution function
4 Density function
6 Uniform distributions
7 Distributions of some functions of random numbers 12
11 Exponential distribution
12 Gamma distribution
13 Normal distributions
15 Generating a random variable with a given continuous distribution
16 Expected value of continuous distributions
17 Expected value of a function of a continuous random variable
18 Median
19 Standard deviation, etc

Part-IV
1 Two-dimensional random variables and distributions
2 Uniform distribution on a two-dimensional set
4 Projections and conditional distributions
5 Normal distributions in two-dimensions
6 Independence of random variables
8 Properties of the expected value, variance and standard deviation
12 Limit theorems to normal distributions
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        Results

        Results of the exam on 8th January
         
Students may come and see their tests: 10th Jan., Wednesday, 10am, H502
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     Results of the 15th January exam:
          EEHL7A: 38 points,  grade = 4
          PX10ZF: 16 points,  grade = 1
         TOM9S6: 17 points, grade = 1
     Students may come and see their exams on 17th January, Wednesday 10 am, H502 

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