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# Probability and statistics

## Early probability

❶As stated above, this is the unit where the two versions of the course differ.

## Probability

Proper statistical treatment of experimental data can thus help avoid unethical use of statistics. Philosophy of statistics involves justifying proper use of statistics, ensuring statistical validity and establishing the ethics in statistics. Here is another great statistics tutorial which integrates statistics and the scientific method. Statistical tests make use of data from samples.

These results are then generalized to the general population. How can we know that it reflects the correct conclusion? Contrary to what some might believe, errors in research are an essential part of significance testing. Ironically, the possibility of a research error is what makes the research scientific in the first place. If a hypothesis cannot be falsified e. If a hypothesis is testable, to be open to the possibility of going wrong. Statistically this opens up the possibility of getting experimental errors in your results due to random errors or other problems with the research.

ROC Curves are used to calculate sensitivity between true positives and false positives. This will help them to understand the nature of what they are studying. The goal of predictions is to understand causes. Correlation does not necessarily mean causation.

Regression analysis and other modeling tools. In research it is often used to test differences between two groups e. Analysis of Variance can also be applied to more than two groups. Check out our quiz-page with tests about:. Oskar Blakstad Feb 13, Retrieved Sep 10, from Explorable.

The first law was published in and stated that the frequency of an error could be expressed as an exponential function of the numerical magnitude of the error, disregarding sign. The second law of error was proposed in by Laplace and stated that the frequency of the error is an exponential function of the square of the error. Daniel Bernoulli introduced the principle of the maximum product of the probabilities of a system of concurrent errors.

Donkin , , and Morgan Crofton Augustus De Morgan and George Boole improved the exposition of the theory. Andrey Markov introduced [21] the notion of Markov chains , which played an important role in stochastic processes theory and its applications. The modern theory of probability based on the measure theory was developed by Andrey Kolmogorov Like other theories , the theory of probability is a representation of its concepts in formal terms—that is, in terms that can be considered separately from their meaning.

These formal terms are manipulated by the rules of mathematics and logic, and any results are interpreted or translated back into the problem domain. There have been at least two successful attempts to formalize probability, namely the Kolmogorov formulation and the Cox formulation. In both cases, the laws of probability are the same, except for technical details.

There are other methods for quantifying uncertainty, such as the Dempster—Shafer theory or possibility theory , but those are essentially different and not compatible with the laws of probability as usually understood. Probability theory is applied in everyday life in risk assessment and modeling. The insurance industry and markets use actuarial science to determine pricing and make trading decisions. Governments apply probabilistic methods in environmental regulation , entitlement analysis Reliability theory of aging and longevity , and financial regulation.

A good example of the use of probability theory in equity trading is the effect of the perceived probability of any widespread Middle East conflict on oil prices, which have ripple effects in the economy as a whole. Accordingly, the probabilities are neither assessed independently nor necessarily very rationally.

The theory of behavioral finance emerged to describe the effect of such groupthink on pricing, on policy, and on peace and conflict. In addition to financial assessment, probability can be used to analyze trends in biology e.

As with finance, risk assessment can be used as a statistical tool to calculate the likelihood of undesirable events occurring and can assist with implementing protocols to avoid encountering such circumstances. Probability is used to design games of chance so that casinos can make a guaranteed profit, yet provide payouts to players that are frequent enough to encourage continued play.

The discovery of rigorous methods to assess and combine probability assessments has changed society. Another significant application of probability theory in everyday life is reliability. Many consumer products, such as automobiles and consumer electronics, use reliability theory in product design to reduce the probability of failure.

The cache language model and other statistical language models that are used in natural language processing are also examples of applications of probability theory. Consider an experiment that can produce a number of results. The collection of all possible results is called the sample space of the experiment.

The power set of the sample space is formed by considering all different collections of possible results. For example, rolling a dice can produce six possible results. One collection of possible results gives an odd number on the dice. These collections are called "events". If the results that actually occur fall in a given event, the event is said to have occurred.

To qualify as a probability, the assignment of values must satisfy the requirement that if you look at a collection of mutually exclusive events events with no common results, e. This course does not require any previous knowledge of statistics. Basic familiarity with algebra such as knowing how to compute the mean, median and mode of a set of numbers will be helpful. See the Technology Requirements for using Udacity.

Free Course Intro to Statistics Enhance your skill set and boost your hirability through innovative, independent learning.

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Learn statistics and probability for free—everything you'd want to know about descriptive and inferential statistics. Full curriculum of exercises and videos.

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This website provides training and tools to help you solve statistics problems quickly, easily, and accurately - without having to ask anyone for help. Learn at your own pace. Free online tutorials cover statistics, probability, regression, survey sampling, and matrix algebra - all explained in.