Axioms/Postulates of Probability

We can use some postulates or axioms to define this probability. Axioms or postulates are forms of basic assumptions that we make to characterize anything that are logically coherent and non-overlapping. Typically, such postulates are derived by considering feasible features that we would like to see in the defined thing. There is no way to prove or disprove these fundamental assumptions. The probability or chance of occurrence of the event A will be defined by the following three postulates.

The Postulates

(i) 0 ≤ P(A) ≤ 1 or the probability of an event is a number between 0 and 1, both inclusive;

(ii) P(S) = 1 or the probability of the sure event is 1;

(iii) P(A1 ∪ A2 ∪ ⋯) = P(A1) + P(A2) + ⋯ whenever A1,A2,... are mutually exclusive [The events may be finite or countably infinite in number]

The characteristic 0≤P(A)≤1 corresponds to the requirement that a relative frequency be between 0 and 1. The fact that an outcome from the sample space happens on every trial of an experiment results in the property P(S) = 1.

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Research Finding: Israeli scientist Affirmed Ivermectin can Reduced of COVID-19 virus among Non-hospitalized Patients

According to recent research from Sheba Medical Center in Tel Hashomer, ivermectin, a parasite-fighting medicine used in third-world nations, could help shorten the duration of infection for those who get coronavirus for less than a dollar a day. Since 1987, the US Food and Drug Administration has approved ivermectin. The drug's creators were awarded the Nobel Prize in Medicine in 2015 for their treatment of onchocerciasis, a condition caused by a parasitic roundworm infestation. It's been used for a variety of conditions over the years, including scabies and head lice. Furthermore, multiple clinical studies in the last decade have begun to demonstrate its antiviral effectiveness against viruses ranging from HIV and the flu to Zika and West Nile. The medicine is also very cost effective. According to a study published in the peer-reviewed American Journal of Therapeutics, ivermectin for alternative treatments costs roughly $0.60 to $1.80 for a five-day course in Bangladesh. In Israel, a day can cost up to $10, according to Schwartz.

Prof. Eli Schwartz, founder of Sheba's Center for Travel Medicine and Tropical Disease, launched a randomized, controlled, double-blinded research from May 15, 2020, to January 31, 2021, to see if ivermectin may reduce viral shedding in nonhospitalized patients with mild to moderate COVID-19. In Schwartz's study, 89 adults over the age of 18 who had been diagnosed with coronavirus and were staying in state-run COVID-19 hotels were randomly assigned to one of two groups: 50% received ivermectin and 50% received a placebo, based on their weight. Three days in a row, an hour before a meal, they were given the pills. The subjects were checked using a routine nasopharyngeal swab PCR test to see if their viral load had decreased by the sixth day, which was the third day after the treatment ended. Every two days, they were swabbed.

Result

By day six, nearly 72% of subjects treated with ivermectin had tested negative for the virus. Those who received the placebo, on the other hand, only tested negative 50% of the time.Furthermore, the study looked at culture viability, or how infectious the patients were after six days, and found that only 13% of ivermectin patients were infectious, compared to 50% of the placebo group - nearly four times as many.

“First and foremost, our research reveals that ivermectin has antiviral activity,” Schwartz said. “It also demonstrates that a person has an almost 100 percent chance of becoming noninfectious in four to six days, which could lead to these patients spending less time in isolation. This has the potential to have a massive economic and social impact.”

Research with Similar Findings

Other similar studies, while not all of them conducted to the same double-blind, placebo-controlled criteria as his, indicated a positive effect of ivermectin treatment, according to Schwartz. He noted that his research did not establish that ivermectin is useful as a preventive, meaning that it can prevent sickness, nor that it reduces the likelihood of hospitalization. Other research, he added, have found similar evidence.

“A review by the Front Line COVID-19 Critical Care Alliance summarized findings from 27 studies on the effects of ivermectin for the prevention and treatment of COVID-19 infection, concluding that ivermectin ‘demonstrates a strong signal of therapeutic efficacy' against COVID-19,” according to a study published earlier this year in the American Journal of Therapeutics.

Controversy

IVERMECTIN, however, is not without controversy, and despite high coronavirus levels around the world, neither the FDA nor the World Health Organization have approved it for use in the fight against the virus.

Prof. Ya'acov Nahmias of the Hebrew University of Jerusalem has questioned the drug's safety. In an earlier interview, he stated, "Ivermectin is a chemical medicinal drug with severe hazards associated with it." “We should be extremely cautious about administering this type of drug to treat a viral infection that the great majority of people will recover from without it.”

The FDA announced on its website that it had received "several reports of patients who required medical assistance and were hospitalized after self-medicating with ivermectin." It added that the "FDA has not approved ivermectin for use in treating or preventing COVID-19 in humans." “For some parasitic worms, ivermectin tablets are approved in very particular doses, and there are topical (on-the-skin) versions for head lice and skin problems like rosacea. Ivermectin isn't an antiviral medication (a drug for treating viruses). Taking high amounts of this medicine is risky and can result in significant consequences.”

Merck Co., which manufactured ivermectin in the 1980s, has been the most vocal opponent of the medicine. “Company scientists continue to carefully analyze the findings of all available and emerging studies of ivermectin for the treatment of COVID-19 for evidence of efficacy and safety,” the company said in a public statement regarding ivermectin on its website in February. Our study has shown no scientific basis for a potential therapeutic impact against COVID-19 from pre-clinical studies, no substantial evidence for clinical activity or clinical efficacy in patients with COVID-19 disease, and a concerning absence of safety data in the bulk of investigations.”

Conclusive Statement

Oxford University announced a big trial on the effectiveness of ivermectin last month. Schwartz said he became interested in ivermectin research about a year ago, "when everyone was seeking for a new medicine" to treat COVID-19 and a lot of work was being put into studying hydroxychloroquine, so he decided to join the effort. “I decided to go for it because ivermectin was on my shelf, we were using it for tropical infections, and there were clues it might work,” he added.

Around the same time, researchers in various parts of the world began looking into the medicine. However, when they began to observe positive outcomes, no one wanted to share them, according to Schwartz. He stated, "There is a lot of opposition." “We tried to publish it, but three publications turned it down. Nobody wanted to know about it. You have to wonder why when the rest of the world is suffering.” Large Pharma doesn't want to deal with it since "this medicine will not yield any big economic profits," he claimed.

And delaying the use of ivermectin could lengthen the time it takes for the globe to learn to live with the virus, he added. The researchers said in the American Journal of Therapeutics, "Identifying existing treatments that can be re-purposed against COVID-19 [and] that already have a known safety profile over decades of usage could play a critical role in slowing or even stopping the SARS-CoV-2 pandemic." “Using repurposed drugs may be especially significant because vaccination may take months, if not years, for a large portion of the world's population, particularly among low- and middle-income populations.”

This is credit to MAAYAN JAFFE-HOFFMAN as the author of this work.

Reference

https://www.jpost.com/health-science/israeli-scientist-says-covid-19-could-be-treated-for-under-1day-675612

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90 serious Covid-19 patients treated with the new drug, 93 percent were released in five days or less

Statistical Report: Out of 90 serious Covid-19 patients treated with the new drug, 93 percent were released in five days or less

In a Phase II trial for an Israeli COVID drug, 29 out of 30 moderate to severe patients recovered within days.

In a Phase II trial of the medication, 93 percent of 90 coronavirus severe patients treated in multiple Greek hospitals with a new drug created by a team at Tel Aviv's Sourasky Medical Center were released in five days or less.

The results of the Phase I experiment, which was done in Israel last winter and saw 29 out of 30 patients in moderate to serious condition recover within days, were confirmed in the Phase II trial.

Prof. Nadir Arber stated, "The main purpose of this study was to prove that the medicine is safe." “To yet, no serious side effect has been observed in any patient from either group.” Because Israel lacked enough relevant patients, the experiment was held in Athens. Prof. Sotiris Tsiodras, Greece's coronavirus commissioner, was the lead investigator.

The medicine was developed by Arber and his team, which included Dr. Shiran Shapira, based on a molecule called CD24 that the professor has been studying for 25 years and is naturally present in the body.

“It's vital to keep in mind that 19 out of every 20 COVID-19 individuals do not require treatment,” Arber added. “After a five-to-twelve-day interval, about 5% of the patients begin to deteriorate.”

An overactive immune system, often known as a cytokine storm, is the primary cause of clinical deterioration. In COVID-19 individuals, the immune system begins to assault healthy cells in the lungs.“This is precisely the issue that our drug addresses,” he explained.

CD24 is a tiny protein that is linked to the cell membrane and has a variety of activities, including regulating the cytokine storm process.Arber emphasized that their medication, EXO-CD24, does not influence the immune system as a whole, but rather focuses on one specific mechanism, assisting in its restoration.He explained, "This is precision medicine." “We are overjoyed that we have discovered a way to combat the disease's physiology.”

The team is now ready to begin the study's final phase.“As encouraging as the early findings of a treatment may be, no one can be certain of anything until the results are compared to those of patients who receive a placebo,” he said. Arber stated, "We plan to finish it by the end of the year." If the findings are confirmed, he promises that the treatment will be available soon and at a low cost.“Moreover, success could pave the way for many more ailments to be treated,” he added.

This is credit to ROSSELLA TERCATIN as the author of this work.

Reference

https://www.jpost.com/health-science/covid-90-percent-of-patients-treated-with-new-israeli-drug-discharged-in-5-days-675961?fbclid=IwAR2hzKwm3Kh7Gv5uRYOss4NgUFb4k89sz84s2bV2YJnpHItzyUFfTi_Spx8

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Research shows about Ivermectin to COVID-19

Introduction to Probability

HISTORY OF PROBABILITY

Probability as a branch of mathematics has a long history, dating back over 300 years, when it was first applied to situations concerning games of chance. Many books are dedicated solely to probability, but our goal is to focus on the aspects of the subject that have the greatest immediate influence on statistical inference difficulties.

The present mathematical theory of probability can be traced back to attempts by Gerolamo Cardano in the sixteenth century and Pierre de Fermat and Blaise Pascal in the seventeenth century to examine games of chance (for example the "problem of points"). Their motivation stemmed from an issue regarding games of chance provided by the chevalier de Méré, a notably philosophical gambler. When a game of chance is stopped, De Méré inquires about the right allocation of stakes. Let's say two players, X and Y, are playing a three-point game with 32 pistoles each, and they're interrupted when X has two points and Y has one.

Pascal thought Fermat's solution was too complicated, so he recommended solving the problem in terms of the quantity now known as "expectation," rather than probability.

Games of chance like this one served as model problems for the theory of chances in its early stages, and they are still used in textbooks today. Pascal's posthumous work on the "arithmetic triangle," which is now associated with his name (see binomial theorem), demonstrated how to calculate numbers of combinations and combine them to solve basic gambling difficulties.

Girolamo Cardano, an Italian mathematician, physician, and gambler, estimated chances for games of chance by counting up equally likely occurrences more than a century ago. However, his small work was not published until 1663, by which time the elements of the theory of chances were well known among European mathematicians.

PROBABILITY

Probability is the study of calculating the chances of something happening. At its most basic level, it is concerned with the roll of a dice or the fall of cards in a game. Probability, on the other hand, is critical to both science and everyday life. It's used for a variety of things, like weather forecasting and figuring out how much your insurance premiums would cost. Probability is the scientific study of randomness and uncertainty. The study of probability gives methods for calculating the chances, or likelihoods, of various outcomes in any situation where one of a number of possible outcomes could occur.

In both written and spoken contexts, the language of probability is frequently utilized in an informal manner. For example, “It is likely that the Dow Jones average will increase by the end of the year,” or “It is likely that the Dow Jones average will climb by the end of the year.” “The incumbent has a 50–50 likelihood of seeking reelection,” says the expert. “It's likely that at least one component of that course will be given next year,” says the professor. “The odds favor a rapid resolution of the strike,” and “at least 20,000 concert tickets are expected to be sold.”

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SAMPLE SPACE AND EVENTS OF AN EXPERIMENT
AREAS UNDER THE NORMAL CURVE

What is Statistics?

Statistics?

How do we define the word statistics? The word statistics has more than one meaning. We encounter it frequently in our everyday language. The origin of the sources we shall use in the definition may be traced to the following authors, of which have very little in common meaning about statistics.  

Reston, (2004), the word statistics simply refers to a mass of data or a collection of facts and figures. The grades of students in the registrar’s office, entrance examination results of incoming freshmen in certain universities or colleges, the average temperature and average rainfall per month, weekly sales of a company A are such statistics in nature.

Freund, et, al. (1986) and Nocon, et, al. (2000), defines statistics as a branch of mathematics that deals with the theory and methods of collection, analysis, interpretation, and presentation of data. As such, the data may be categorical or numerical in nature.

Walpole, (2000) and Lind, et, al. (2000) defines as a science that is concerned with the concepts and techniques employed in the collection, presentation, analysis and interpretation of data to assist in making more effective decisions.

Statistics is the branch of science that deals with the collection, presentation, summarization, analysis, and interpretation of data.

Statisticians

Are professionals who are trained to provide crucial guidance in determining what information is reliable and which predictions can be trusted through the application of statistical methods. Furthermore, it helps determine the sampling and data collection methods, monitors the execution of the study and the processing of data, and advice on the strengths and limitations of the results (www.amstat.org). The word statistician is used to refer to collect and analyze data, and then calculate results using a specific design. One who draws conclusions and makes decisions in the face of uncertainty. They are present behind the scenes in every field of scientific endeavor. The tasks of statisticians include Agricultural and Animal Sciences, Medical Sciences, Business areas, Engineering, Education, Economics, Mathematics, Banking, Accounting, and Auditing, Natural and Social Sciences, etc...

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>Overview about Statistics

>Parameter and Statistics, Population and Sample, Descriptive Statistics and Inferential Statistics

INTRODUCTION TO STATISTICS

Learning Objectives:

Ø  define what is meant by statistics and statistician?

Ø  explain what is meant by variables and types of variables.

Ø  distinguish between a qualitative variable and a quantitative variable.

Ø  differentiate between descriptive statistics and inferential statistics.

Ø  simplify and evaluate the expressions involving summation notation

Introduction

The word statistics is most popular through radio, television, newspapers, and even magazines. Statistics stress analysis of data to generate and facilitate the process of decision – making.

> For the last decade, there has come up among businessmen, policy makers, researchers, economists in government, sociologist, education, psychology, medicine, and business circles, a growing realization of the importance of statistics in policy and decision – making. As a result, many colleges and universities have included statistics in their curricular offerings.

The improvement of quality in the industry among most progressive country has occurred in the early nineteen and twenty first century. The success of the Japanese “industrial miracle” has been attributed to the use of statistical methods and statistical thinking among management personnel (Walpole, 2002).

Statistics is now an active intellectual field of study, the fundamental discoveries may alter statistical practice during the lifetime of the readers of this book (Kenny, 2002).

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>SAMPLE SPACE AND EVENTS OF AN EXPERIMENT

>AREAS UNDER THE NORMAL CURVE

>INTRODUCTION to PROBABILITY

>Parameter and Statistics, Population and Sample, Descriptive Statistics and Inferential Statistics