Topic probability and its application

The probability theory gives an idea of the likelihood of occurrence of various events resulting from a random experiment in terms of quantitative measures ranging from zero to one.. The

BỘ GIÁO DỤC VÀ ĐÀO TẠO TRƯỜNG ĐẠI HỌC KINH TẾ QUỐC DÂN

-Subject: Business Statistics Group Mid-Term Assignment Topic: Probability and its application Class: Advanced Finance 63C Group 4

1 Nguyễn Khương Đan

2 Lê Thu Trang

3 Nguyễn Phúc Thái An

4 Nguyễn Thanh Mai

5 Bạch Minh Huyền

6 Bùi Gia Linh

7 Vũ Minh Hạnh

Assoc Prof : Trần Thị Bích

Hà Nội, 2023

TABLE OF CONTENTS

1 INTRODUCTION 3

1.1 Definition of probability 3

1.2 The necessity of probability 3

1.3 Application of probability 4

2 ARTICLE AND SOURCES ANALYSIS 5

2.1 Article summary 6

2.1.1 Issue of interest 6

2.1.2 Purpose of the article 6

2.1.3 Methodology 6

2.1.4 Conclusion 9

2.2 Techniques used in the article 9

2.3 Additional sources 11

3 DATA ANALYSIS 18

3.1 Database 18

3.2 Data analysis 19

3.2.1 Age analysis 19

3.2.2 Pizza analysis 20

3.2.3 Probability of customers’ returning 25

3.3 Recommendation for manager 26

4 CONCLUSION 27

REFERENCES……… 27

1 INTRODUCTION

1.1 Definition of probability

In our daily lives, the terms "probability" and "chance" are frequently used Probability theory was developed in the 17th century It evolved from games such as coin tossing, dice throwing, and drawing a card from a pack Antoine Gornband first became interested in this field in 1954 Many statisticians after him attempted to refine the former's concept The term "probability" has evolved into one of the most fundamental statistical tools Without the

probability theorem, statistical analysis can become paralyzed The probability

of a given event is defined as its expected frequency of occurrence among events of a similar type The probability theory gives an idea of the likelihood of occurrence of various events resulting from a random experiment in terms of quantitative measures ranging from zero to one The probability of an

impossible event is zero, while the probability of a certain event is one

1.2. The necessity of probability

In everyday life, the concept of probability is extremely important This important concept underpins statistical analysis Probability, in fact, serves as a substitute for certainty in modern science

Predictions can benefit greatly from probability theory Estimates and

predictions are critical components of research We make estimates for further analysis using statistical methods As a result, statistical methods are heavily reliant on probability theory It is concerned with planning and controlling, as well as the occurrence of various types of accidents

It is essential to understand probability and statistics in today's society, when statistical information and interpretation abound in print and electronic media The purpose of probability and statistics education should be to prepare students

to be critical users of probability and statistics, able to apply its procedures and concepts to real-world issues

1.3. Some applications

Probability is the measurement of the likelihood of an event occurring

Probability has a wide range of applications Several real-world uses of

probability are given below

a) Forcasting the weather

Meteorologists use various devices and technologies to collect data on weather and its variations across the world They collect meteorological data from across the world to estimate temperature changes and weather conditions for a specific hour, day, week, month, and year

b) Traffic signals

It's built into the signals because the people who design and install them know the typical amount of pedestrians who need to cross the street and the average number of automobiles in a certain region

If you take a pen and paper and write down all the alternatives, you can grasp the flow of traffic in a city and even predict the amount of green lights you'll finish up with

c) Medical diagnosis

If you have a cough, your odds of having an unusual, deadly disease are quite low as compared to coughing due to simple throat irritation, a simple infection, or something else relatively banal Physicians must thoroughly comprehend false positives and false negatives if they want to diagnose patients Every day, they treat dozens, if not hundreds, of patients In order to treat patients efficiently, doctors employ a variety of mathematical strategies in their everyday practice

d) Gamblings and games

The game of cards Rummy makes use of probability, as well as

permutations and combinations, to predict which cards will end up on the table Another amazing use of probability in real life is poker odds Probability is used by players to evaluate their possibilities of having a good or terrible hand, as well as whether they should wager more or just fold their cards

Card games rely heavily on probability and statistics, which is why poker

is so difficult There are times when you are dealt a lousy hand and there

is nothing you can do about it Unless you're brave and can bluff your way out of a jam

e) Election results

Election authorities utilize historical data to determine how a region voted

in the past in order to predict who they would vote for this time They combine this with current trends and surveys, as well as a lot of

arithmetic, to determine who will win

f) Lottery probability

There is one strategy to ensure that you win the lotto 100 percent of the time According to probability theory, the only way to win the lottery is to play it When you play the lottery, you have an independent probability frequency, similar to a coin flip, and you can win or lose

g) Business

The marketing persons or salespersons promote the products to increase sales They use the probability technique to check how much the

particular product is going well in the market or not The probability technique helps to forecast the business in future

2 ARTICLE AND SOURCES ANALYSIS

2.1. Article summary

2.2. Techniques used in article

2.3 ADDITIONAL SOURCES

2.4 Article 2: Drought Severity Assessment Based on Bivariate Probability Analysis

Harris Vangelis· Mike Spiliotis· George Tsakiris

Springer Science + Business Media

Issue

According to estimates, the number of afflicted persons in EU nations has grown by 20% over the last three decades Drought is a natural danger, however

it causes an imbalance in the water supply owing to increased

evapotranspiration and insufficient precipitation, resulting in decreased water availability The study describes the severity of drought conditions using a

simple computational technique based on a bivariate drought index.Purpose

Using the assistance of bivariate probability analysis, this work describes a straightforward computational method for determining the severity of drought conditions using a bivariate drought index

Method

When there are two independent random variables, bivariate probability is the likelihood that an event will occur This type of data analysis is useful in risk management

The P/PET (precipitation/potential evapotranspiration)-based RDI (The Reconnaissance Drought Index) is investigated as a bivariate index in this work

by a stringent probabilistic analysis in the event that both P and PET have a normal distribution The suggested method can also be used for reference periods that are less than a year (such as 3, 6, or 9 months), provided that the normality assumptions for the distributions of P and PET, both individually as well as jointly, are true Users should continue to utilize the standardized RDI in its original proposal, which assumes that P/PET ratio often follows a skewed distribution, in the event that these assumptions are incorrect

Application

The computation of the probability for each annual ratio ai12 may allow us to measure the severity of the drought in a given year, which is a key application

of the suggested methodology

The usage of RDI expressions makes it necessary to look at the correlation between P and PET since they are observed separately (as continuous variables) The formula for calculating the a(i)k for the year I and a reference period of k (months) is:

Subsequently, a(i)k becomes a new variable, and RDI is the monthly sum of a(i)k Next, the outcome of a(i)k indicated by the cumulative probability F(k) in the chart can be evaluated as follows:

Given the results of the analysis above, it is clear that the cumulative likelihood and, hence, the return period of drought can be calculated if the time series for lengthy historical record of P and PET are available

For all of the aforementioned reference periods and stations, a correlation test between P and PET was run The findings in Table 1 demonstrate the correlation between the two variables

Use the frequency table to convert the number in the table above to forecast the return periods of 5, 10, 20, and 50 years at Helliniko, Larissa, Heraklion, and Naxos

Conclusion

Drought requires a preparation planning method to reduce the susceptible of the affected system and raise its resilience

The outcome is used to determine how much drought protection the preparation plan should give Prioritizing activities, measurements, and engineering projects

is also critical for implementing proactive techniques for mitigating droughts and water shortages

2.5. Article 3: Statistical Methodology for Profitable Sports Gambling

Fabián Enrique Moya B.Sc., Anáhuac University, 2001

Issue

When a bookmaker sets odds on a certain market, it is implicitly estimating the likelihood of various events For some markets, it is feasible that the bookmaker will give incorrect probability estimations If a gambler can discover poorly judged markets, he or she may be able to transform sports gambling into a profitable pastime

Purpose

With the help of historical data, this research seeks to increase the potential for forecasting the minimum assured rainfall By determining when to plant crops,

it is viewed as an early warning system that aids in agricultural planning

Technique

The function NORMDIST (MS Excel 5.0) was used to compute the chance of rainfall at various levels and to calculate the expected quantity of precipitation

at various probability levels Following is the method for calculating the normal probability density function from the mean and standard deviation

Where, x = Variable for which the distribution is required μ = Arithmetic mean

of the distribution σ = Standard deviation of the distribution

Application

The research team determines the probability of rainfall from the average (the mean) of the weekly and monthly precipitation in order to identify and predict the times with the greatest and lowest amounts of precipitation They use this data to make graphs and charts showing probability distributions Probability (P

%) was displayed on a semi-log scale for weekly, monthly, seasonal, and yearly time intervals A power equation of the second degree was fitted to predict projected precipitation at different probability levels

On the basis of rainfall analysis of rainfall data of Raipur, it can be inferred that

at 75% probability level the highest rainfall 25.83 mm received by 33rd week and lowest rainfall received by 39th week i.e 7.41 mm The climatic season is varied in nature and found that at 75% probability the monsoon season received the highest rainfall Hence the valuable information obtained from the analysis

of rainfall in present study can be used for crop planning, designing of soil and water conservation structure in the Raipur region

3 DATA ANALYSIS

4 CONCLUSION

It is clear from the study and data analysis in Probability that the application of probability is diverse It is critical in forecasting the behavior of random variables Probability is used to forecast various occurrences in our lives so that decisions can be more dependable, reduce risks, and make decisions more practical and capable of producing the greatest results

REFERENCES

https://www.byjusfutureschool.com/blog/examples-of-probability-in-real-life/