Matehematics A4 in English - Probability Theory
2017 Spring
Andras Vetier

Requirements

Interactive Electonical Probability Text Book 

Suggested textbooks in probability

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Week 01:
2017-02-07___01_relfreq_prob.xlsx
2017-02-07___02_two_dice.xlsx
2017-02-07___03_two_dice_LESS_EXPERIMENTS.xlsx
2017-02-07___04_file_modification.xlsx

2017-02-08___01_distribution_of_the_number_of_boys_out_of_10_children.xlsx
2017-02-08___02_probability_of_an_interval.xlsx

Homework:
1. Study chapters 2, 3, 5 of   http://math.bme.hu/~vetier/df/Part-I.pdf
2. Solve the problem given in file  2017-02-08___03_Home-work.xlsx
3. 100 persons are chosen at random in a country.
      a) Construct - with Excel -  a table and a figure for the distribution of the number of men.

  What is the probability that the number of men is
      b)  equal to 55?
      c) less than 55?
      d) greater than 40 but less than 60?


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Week 02:
2017-02-14___01_Bus_Metro.xlsx
2017-02-15___01_Bus_Metro_EVENT2.xlsx
2017-02-15___02_Bus_Metro_EVENT1__AND__EVENT2.xlsx
2017-02-15___03_Bus_Metro_EVENT1__OR__EVENT2.xlsx
2017-02-15___04_Bus_Metro_Vomplement_of_EVENT1.xlsx

Homework:
1.   Study Chapters  2 - 8  of  Part-I  until the bottom of page 24 from   
      http://math.bme.hu/~vetier/df/Part-I.pdf

2.  Solve the following problems from 

     http://math.bme.hu/~vetier/df/Part-I__PROBLEMS.pdf

        8, 9, 10, 11,

        37, 40, 41,
        64, 65,
        85, 88,
        97, 100, 101
We will discuss the solutions of the problems which turn out to be intersting or difficult or problematic on our lesson next Tuesday


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Week 03:
2017-02-21___01_Sick_if_diagnosed_sick.xlsx
2017-02-22___01_How_many_people_go_for_the_hike.xlsx
2017-02-22___02_Calc_prob-s_with_binomial_distribution.xlsx
2017-02-22___03_Extra_tickets_sold.xlsx
2017-02-22___03_Homework.xlsx
2017-02-22___04_HLOOKUP_command.xlsx
2017-02-22___10_How_many_people_go_for_the_hike_SIMULATED_USING_VLOOKUP_COMMAND.xlsx

Homework:
Study Chapters 1-4  of  Part-II  from  http://math.bme.hu/~vetier/df/Part-II.pdf

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Week 04:


2017-02-28___01_First_success.xlsx

2017-02-28___02_First_success.xlsx
2017-02-28___03_Negative_binomial_distributions.xlsx
2017-02-28___04_limit_statement.xlsx


2017-03-01___01_Binom-Poisson.xlsx
2017-03-02___02_Expected_value.xlsx


Homework:
Study and learn Chapters 1-9  and  13-16  of  Part-II  from  http://math.bme.hu/~vetier/df/Part-II.pdf
Solve one or two problems from
Chapters 1-9  and  13-16  of   http://math.bme.hu/~vetier/df/Part-II__PROBLEMS.pdf
(at least one from each of those chapters)

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Week 05:

2017-03-07___01_Expected_value.xlsx
2017-03-07___02_Variance_and_standard_deviation_of_a_data-set.xlsx
2017-03-07___03_Variance_and_standard_deviation_of_a_random_variable.xlsx

2017-03-08___01_Binomial_random_variable.xlsx
2017-03-08___02_Binomial_random_variable.xlsx
2017-03-08___03_Arbitrary_distribution_on_0-1-2-3-4-5.xlsx
2017-03-08___04_Arbitrary_distribution_on_0-1-2-3-4-5.xlsx

Homework:
Study and learn Chapters  16-18  of  Part-II  from  http://math.bme.hu/~vetier/df/Part-II.pdf
Study and learn Chapter  19   of  Part-III  from  http://math.bme.hu/~vetier/df/Part-III.pdf

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As it was told before, 14 March, Tuesday - no lesson will be.
Instead of that our lessons from 28 Feb to 22 March
are 15 minutes longer, they start at 10:15 and end at 12:00

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Midterm Test1: 22 March, Wednesday, during our lesson
Midterm Test2: 26 April, Wednesday, during our lesson

Material of Test1: What we have taken until now
   - Problems to solve (students may work with or without Excel)
   - Questions (about important notions, definitions, statments) to be answered with sentences
No proofs of theorems will be asked


On our Tuesday lesson before the test, students - naturally - may ask any questions.


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Week 08:
2017-03-28___02_NON_unformly_distributed.xlsx
2017-03-28___03_NON_unformly_distributed.xlsx
2017-03-28___04_Square_of_a_random_number.xlsx
2017-03-28___05_Max_of_3_random_numbers.xlsx
2017-03-28___06_Largest_of_10_random_numbers.xlsx
2017-03-28___07_Second_Largest_of_10_random_numbers.xlsx
2017-03-28___08_Third_Largest_of_10_random_numbers.xlsx

Homework:
Learn Chapters 1, 2, 4, 6, 7, 10 from  http://math.bme.hu/~vetier/df/Part-III.pdf
Find F(x) and f(x) of the Third_Largest_of_10_random_numbers (Complete the Excel file as well). Solve it by tomorrow.

2017-03-29___01_Random_number_unformly_distributed.xlsx
2017-03-29___02_Random_number_plus_a_constant.xlsx
2017-03-29___03_Random_number_multiplied_by_a_constant.xlsx
2017-03-29___04_Random_number_multiplied_by_a_constant_plus_another_constant.xlsx
2017-03-29___05_The_reciprocal_of_a random_number.xlsx
2017-03-29___06_RND1_times_RND2.xlsx

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Week 09:

2017-04-04___01_Expon_distr.xlsx
2017-04-05___01_Norm_distr.xlsx
2017-04-05___02_An_interpretation_of_the_CENTRAL_LIMIT_THEOREMS.xlsx
2017-04-05___03_Simulation_of_a_normally_distr_random_variable.xlsx

Homework:
Learn Chapters 11, 13, 15, 16, 17 from  http://math.bme.hu/~vetier/df/Part-III.pdf
 

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Week 10:

2017-04-11___01_Properties_of_expected_value______
2017-04-11___02_Twentyfive_bulbs_in_our_celler
2017-04-11___03_One-_two-_three-sigma_rules
Homework:
Learn
Chapter 19 from  http://math.bme.hu/~vetier/df/Part-III.pdf

and
Chapter 8 from  http://math.bme.hu/~vetier/df/Part-IV.pdf
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Week 11:
2017-04-18___01_First_and_Last_arrival_times.xlsx
2017-04-18___02_two_bulbs.xlsx

Homework:
Learn from 

http://math.bme.hu/~vetier/df/Part-IV.pdf

  
Chapter 1 pages 2-3 only
   Chapter 2  
   Chapter 3

2017-04-19___01_First_and_Last_arrival_times.xlsx
2017-04-19___02_Secondt_and_Third_arrival_times.xlsx
2017-04-19___03_Secondt_and_Third_arrival_times_between_0_and_2.xlsx
2017-04-19___04_Coins_and_dice.xlsx

Homework:
Write the correct command into the cell  E10  of the file
Homework:2017-04-19___05_Homework.xlsx
and give your explanation in the pink cells.
Then send your solution to vetier@math.bme.hu as an attached file.
Let the subject of the letter be: Simulation command.

If your command and explanation are correct,
you get extra points to be included in your final grade.


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Week 12:

2017-04-25___01_Expected_value_of_the_product.xlsx
2017-04-25___02_Expected_values.xlsx
2017-04-25___03_Expected_values.xlsx
2017-04-25___04_POJECTIONS.xlsx


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Week 13: 2017-05-03___01_Height_Weight.xlsx
2017-05-03___02_HeightWeigh_EigenVect_Proj_CondDist.xlsx
2017-05-03___03_Calculating_conditional_EXPECTED_VALUES__PROBABILITIES.xlsx


Homework:
Learn from
http://math.bme.hu/~vetier/df/Part-IV.pdf 
Chapter 1 pages 2-3 only    Chapter 2

Chapters 4, 5, 6, 8, 11, 12

Using the same parameters as we used in class (see
2017-05-03___03_Calculating_conditional_EXPECTED_VALUES__PROBABILITIES.xlsx)
determine the following probabilities and conditional probabilites:

P( height is between 180 and 190 )

P( height is between 180 and 190 | weight is 65 )

P( height is between 180 and 190 | weight is 70 )

P( height is between 180 and 190 | weight is 75 )

P( height is between 180 and 190 | weight is 80 )

P( height is between 180 and 190 | weight is 85 )

P( height is between 180 and 190 | weight is 90 )

P( height is between 180 and 190 | weight is 95 )

P( height is between 180 and 190 | weight is 100 )

P( height is between 180 and 190 | weight is 105 )

P( height is between 180 and 190 | weight is 110 )


P(  weight is between 80 and 90 )
P(  weight is between 80 and 90 | height is 165 )
P(  weight is between 80 and 90 | height is 170 )
P(  weight is between 80 and 90 | height is 180 )
P(  weight is between 80 and 90 | height is 185 )
P(  weight is between 80 and 90 | height is 190 )
P(  weight is between 80 and 90 | height is 195 )

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Exam_2017_05_10.pdf
Exam_2017_05_10_Solutions.pdf

Exam results:



Exam Total Course


points points grade
AIQYYM
45 84 5
EUQQEM
33 76 4
FYURD8
55 92,5 5
GBBT8T
48 83 5
INSDJ9
36 75 4
O36694
42 86 5
V9PJ70
55 99 5
VDOFVV
26 63 3
XQ7L7J
40 69,5 3

Max exam points: 6 x 2 x 5 = 60

Register, please, for the first exam in Neptun,
and then your
grade will be written into Neptun

If you want, you may see your test: 12 May, Friday 1pm, H502
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Repeated test results:



rep test rep test


1 2
IXU528
8 1 failed the course
HKTDIY
3 0 failed the course
ZZXBFX

17 gets signature

If you want, you may see your test: 12 May, Friday 1pm, H502
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Exams:
22 May, Monday, 10am E1B
12 June,
Monday, 10am E1B
19 June,
Monday, 10am E1B
Students have to register for the exams in Neptun

The first official exam date is May 22.
This is the date for which you may register.
However, students  may come on May 15
The Monday exam will start at 11am in H601.
I hope this change is not a problem for you.

In this case, send me an email to  vetier@math.bme.hu  to let me know that you come on may 15.


May 15 Exam results:



EXAM TOTAL EXAM


points points grade
EUQQEM
50 93 5
ZZXBFX
30 68 3

In order that the grades could be written into Neptun,
students are asked to register for the May 22 exam.


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