Group name the mud hensprobability and statistics theory tổng hợp công thức, lý thuyết xác suất thống kê

MINISTRY OF EDUCATION AND TRAINNING HO CHI MINH UNIVERSITY OF LAW GROUP NAME: THE MUD HENS PROBABILITY AND STATISTICS THEORY Major: Business Administration Subject: Mathematical probabil

MINISTRY OF EDUCATION AND TRAINNING

HO CHI MINH UNIVERSITY OF LAW

GROUP NAME: THE MUD HENS

PROBABILITY AND STATISTICS THEORY

Major: Business Administration

Subject: Mathematical probability and statistics theory Class: 120-QTKD45.1

Lecturer: Trần Thị Bảo Trâm

The list of contributors:

Numbe

r Student Name Student Code Contribution level

1 Đinh Lê Ngọc Điểm 2053401010016 100%

2 Nguyễn Hoài Linh 2053401010044 100%

3 Nguyễn Thị Thanh Nga 2053401010057 100%

Đinh Lê Ngọc Điểm:

 Content Adviser

 Translater

Nguyễn Thị Thanh Nga:

 Content Adviser

 Translater

Nguyễn Hoài Linh:

 Content Presenter

 Mind-map Designer

TABLE OF CONTENTS

I INTRODUCTION 4

II OVERVIEW OF STATISTICAL PROBABILITIES 5

1 WHAT IS STATISTICAL PROBABILITY? 5

2 APPLICATIONS OF PROBABILITY AND STATISTICS 5

a In economics and finance 5

b Games and leisure activities 6

c Sports Strategy 7

d Application of probability in biology: Genetics 7

e Application of probability in exams 8

3 MIND MAP 9

a Mind map of the Probability 9

b Mind map of the Statistics 10

III EXERCISE 11

IV ACKNOWLEDGMENT 14

I INTRODUCTION

In each person, perhaps since childhood, we have always believed in luck, always believe that there's a guardian deity that brings lots of luck, roughly called "fairy" Today, after we get older a touch bit, we all know "statistical probability", we depend on science quite we predict of ourselves, but only know

a bit a few certain aspects So has anyone ever been curious to find out deeply and apply them to measure properly? Let's follow The Mud Hens to find the key that has been hidden for this long

The peregrinations of statistics constitute one of the weightiest and most unpredictable chapters within the history of the transmission of ideas between the natural and social sciences Mathematical statistics has long been idealized

as a possible means for capturing the goblet of the sciences of man, quantification, and applied math were central to the earliest sustained effort during this direction, Condorcet’s social mathematics Laplace’s injection within the Philosophical Essay on Probabilities to “apply to the political and moral sciences the strategy founded upon observation and upon calculus, the tactic which has served us so well within the natural sciences,”1 was already commonplace in 1814 and was frequently invoked throughout the nineteenth century Yet the migration of mathematics from the hard to the soft sciences is merely a component of the career of statistical thinking since the time of Laplace Equally important, and maybe more impressive is that the role of that prominent nineteenth-century scientific discipline, “statistics'', in facilitating the appliance of probabilistic mathematics to the biological and physical domains The statistical probability is sort of a judgment that challenges human intelligence We will only admit that we've heard and known it, but cannot confirm that we've fully understood it The Mud Hens hopes to produce the required knowledge to answer the "we don't know" things through different perspectives Thereby, helping people who haven't, are learning to like and know the way to use it in their own life more

Too long to read on your phone? Save

to read later on your computer

Save to a Studylist

II OVERVIEW OF STATISTICAL PROBABILITIES

1 WHAT IS STATISTICAL PROBABILITY?

Probability is the study of the likelihood that an occasion will occur, and statistics is the analysis of huge data sets, often with the goal of usefully describing this data or drawing conclusions from a few larger data sets supported by a proportional sample These two branches of mathematics may be thought of as two sides of an identical coin: statistics helps you understand the past, and probability helps you employ that knowledge to predict the future! Statistics and probability are essential tools for data science These skills allow you to see if your data collection methods are sound, gather relevant insights from huge data sets, build analytic models that generate usable results, and more Important concepts and skills within the data science context include sampling distribution, statistical significance, hypothesis testing, and multivariate analysis

2 APPLICATIONS OF PROBABILITY AND STATISTICS

You use probability in your

standard of living to form decisions

once you do not know obviously what

the end result is going to be Most of

the time, you will not be doing actual

probability problems, but you may be

using subjective probability to form

judgment calls and determine the most

effective course of action

a In economics and finance

Probability and statistics play an important role altogether in areas of human action Specifically, they're widely used quantitative tools within the fields of economics and finance Knowledge of contemporary probability and statistics is important for the event of economic and financial theories and for testing their validity through robust analysis of real-world data For instance,

probability and statistics can help shape effective fiscal and monetary policies and develop pricing models for financial assets like stocks, bonds, currencies, and derivatives born The importance of developing robust methods for empirical analysis has become particularly important after the recent global financial crisis of 2008, which placed economic and financial theories at the bottom sighting range

b Games and leisure activities

You use probability when playing board,

card, or video games that involve chance You

must consider the possibility of getting the cards

you need in poker or the secret weapons you

need in a video game The ability to get those

tokens or tokens will determine how much risk

you are willing to take For example, the odds

are 46.3 to 1 that you will get three of the same

hand in your poker hand - the chance is

approximately 2% - according to Wolfram Math

World However, the odds are approximately 1.4 to 1 or about 42 percent that you will get a pair Probability helps you assess what is at stake and determine how you want to play the game

c Sports Strategy

Athletes and coaches use probability to determine the best athletic strategies for games and competitions A baseball

coach rates a player's batting average when

placing him on the line-up For example, a

player with an average of 200 hits means

he gets two hits for every 10 dropped A

player with a hitting average of 400 is even

more likely to hit a hit - four out of every

10 drops are basic Or, if a high school

soccer player makes 15 main goal scoring

attempts from more than 40 yards during

the season, he has a 60% chance of scoring

on the next attempt from that distance

d Application of probability in biology: Genetics

As is known, probability theory is widely applied in many fields, including biology, especially genetics At present, genetics is widely applied in life and production, based on the principles of probability, one can predict the expression of certain traits or diseases in the next generation

Human genetic diseases

Human Genetic diseases are diseases that

are passed on from parents to their children

through sex cells (eggs or sperm) Thus the

pathogen originates from within the zygote

(embryo), from the point of origin of life in

the uterine cavity On the chromosomes of the

sperm or egg, there are already disease genes

or it can also be due to an abnormal

chromosomal aberration The application of

probability theory has partly helped to

determine: With how sick parents should

have children, then should they not have

children

Natural family planning

Planning for an early birth will give you more time to think and make the best choices for the whole family Among them can be mentioned the concern about the possibility of having a boy or a girl, whether to have another baby or not

e Application of probability in exams

In 2017, the National High School Exam had a new step, in which Mathematics changed from the form of essay exam to multiple choice Up to now, the story of whether or not to take multiple-choice exams is still a hotly debated topic in the education industry The number of people saying "should"

is quite a lot and the number of people saying "should not" is also not few Therefore, for educators, it is extremely necessary to study the advantages and disadvantages of multiple-choice tests and its disadvantages to be able to use this form Besides, another department also studies this exam form to discover tricks to be able to complete the test well

3 MIND MAP

a Mind map of the Probability

b Mind map of the Statistics

III EXERCISE

In a fruit shop, due to lack of baskets to store, the store put 3 types of oranges together in two baskets

Basket one has 30% Seville Orange, 50% Navel Orange, and 20% Clementine Knowing in the basket one sour taste of Seville Orange is 50%, sour taste of Navel Orange is 80% and sour taste of Clementine is 10%

Basket two has 40% Seville Orange, 30% Navel Orange, and 30% Clementine Knowing in the basket two sour taste of Seville Orange is 60%, sour taste of Navel Orange is 50% and sour taste of Clementine is 10% Ms A is a customer who comes to buy fruit from this store

a Miss A chooses oranges from basket one Calculate the probability that Miss A chooses the sour taste ?

b Suppose there are 30 Seville Orange in basket two, and Ms A chooses 9

at random Find the probability that out of the 9 picks has 3 are sour

c Suppose in basket two there are 20 Navel Orange Miss A chooses 8 Navel Orange in basket two Find the probability that there are 3-5 sour oranges

d Ms A arbitrarily chooses 3 balls in the first basket On average, how many sour fruits are there?

e Assume the amount of Vitamin in orange is a random variable with a standard deviation of 4.19mg Analysis of 50 oranges obtained an average vitamin content of 30mg With 97% confidence, estimate the average amount of Vitamins in an orange

The store calculates that the average amount of money customers come to buy oranges per week is 25,000 VND A random survey of 25 customers found that the average amount of orange customers was 24,000 VND, s = 2 At the 5% level of significance, will the purchasing power of customers in the situation of the Covid epidemic decrease or not?

SOLUTION

a The probability that Miss A chooses the sour taste of orange:

0,5.0,3 0,8.0,5 0,1.0,2 + + 0,3 0,5 + +0,2 =0,57

b Randomly select 9 oranges out of 30 ⇒Sample space: C 30

9

Let B be the event that out of 9 picks, 3 are sour

⇒ P(B)=C18

3

.C 12 6

C309 ≈ 0,05

c Miss A chooses 8 Navel Orange in basket two ⇒ sample space: C 20

8

Let D be the event that there are i mediocre oranges with a sour taste

P(D3)=C103.C 105

C 20

8 ≈ 0,24

P(D4)=C10

4

C 10

4

C208 ≈ 0,35

P(D 5 )=C10

5

.C 10

3

C208 ≈ 0,24

The probability to find is: 0,24 0,35 0,24 0,83 + + =

d Let X be a random variable that indexes sour oranges

Let A be the event that Seville Orange has a sour taste

Let B be the event that Navel Orange has a sour taste

Let C be the event that Clementine has a sour taste

⇒ P( X=0)= P (A ) P(B) P(C )= 0,5.0,8.0,1=0,0

P( X=1)= P( A B C+ A B C + A B C )= 0.09+0,36+0,01=

P( X=2)= P( A B C+ A B C + A B C )= 0,36+0,01+0,04=

P( X=3)=1 −0,04 − 0,46 −0,41 0,09 =

Probability distribution table of X:

⇒ E(X )=0.0,04+1.0,46+2.0,41+3.0 09=1,55

On average has 1,55 sour oranges out of the total number of oranges

e Let be the average amount of Vitamin in 1 orange

n=50 ≥30 , σ known ⇒ Case 1

x=30 , 1− α=97 % ⇒φ(t)=α 1 − α

2 =

0,97

2 =0,485 ⇒tα =2,17

ε=tα.σ

√n=2,17.

4,19

√50=1,29

On average μ ∈(x − ε ; x+ε)=( 30 − 1,29 30 ; +1,29 )=( 28,71 ;31,29

f Let a be the average amount of money customers bought oranges

Set H: μ=25; H : μ<25

n=15<30 , σ unknown ⇒ Case 4

α=5 % ⇒2α=0,025 ⇒t 140,025

=2,145

t=|24 25 − |

2 .√15 1,936 =

t =1,936< t140,025 =2,145 ⇒ accept H

Therefore, the purchasing power of customers decreases during the Covid epidemic situation

IV ACKNOWLEDGMENT

To have the knowledge like today, The Mud Hens would really like to express our sincere thanks to lecturer Tran Thi Bao Tram - who has accompanied us during the hobby Within the process of studying and understanding applied mathematics and Statistics, The Mud Hens has received plenty of attention, help, and guidance from her She helped us accumulate more knowledge to grasp more deeply and be able to apply more in our studies and add to the near future

Perhaps knowledge is limitless and every person's acquisition of data may have certain limitations Therefore, within the process of creating and completing the lesson, we are going to inevitably make mistakes and omissions

we actually forestall receiving your suggestions to achieve more knowledge and skill for ourselves for the upcoming subjects

Finally, The Mud Hens would really like to send her best wishes, wishing her lots of health, happiness, and success on her teaching career path