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
------------------------------------
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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