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### Statistics and probability,Basic probability terms

AdKöp Perspectives In Mathematical Science I: Probability And Statistics E-bok AdProbability and statistics. Master of science, data analysis, machine learning & more. Learn how to understand probability and statistics. Find the right course for you today! Educational aims & objectives The aim of the module is to introduce the basic concepts and Probability and Statistics I: A Gentle Introduction to Probability This course provides an (Image by Jerry Orloff and Jonathan Bloom.) Course Description This course provides an ... read more

Comienza el 2 nov. Me gustaría recibir correos electrónicos de GTx e informarme sobre otras ofertas relacionadas con Probability and Statistics I: A Gentle Introduction to Probability. Sobre este curso. Lo que aprenderás. Preguntas frecuentes. Formas de realizar este curso. edX For Business. A tu ritmo. Hay una sesión disponible: ¡Ya se inscribieron 14,! Una vez finalizada la sesión del curso, será archivado Abre en una pestaña nueva. Probability and Statistics I: A Gentle Introduction to Probability. Acerca de. Inscríbete ahora Comienza el 2 nov. Sobre este curso Omitir Sobre este curso. De un vistazo Institución: GTx Tema: Análisis de datos Nivel: Intermediate Prerrequisitos: You will be expected to come in knowing a bit of set theory and basic calculus.

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Probability and statistics are two branches of mathematics concerning the collection, analysis, interpretation, and display of data in the context of random events. They are often studied together due to their interrelationship. In order to discuss probability, it is important to be familiar with the terminology used. Below are some of the terms commonly used in probability. The outcome of a random event, such as the flip of a coin, cannot be determined with certainty before the event has occurred. However, if the possible outcomes are known in this case heads or tails probability theory allows us to predict the chance of a given outcome occurring. In its most common usage, the probability of something occurring is the proportion or fraction of times that a particular outcome is likely to occur.

Probability is represented by a numerical value between 0 and 1 which describes how likely an event is to happen. A probability of 0 indicates that it is impossible for an event to happen while a probability of 1 means that it is sure to happen. Probability is also often expressed using percentages. For example, a 0. There are a number of ways to determine the probability of an event. One way is to speculate the probability of the event. For example, assuming that a coin is fair, we can speculate that there is a 0. For a perfectly balanced 6-sided die, the possibility of each side showing up is the same.

Therefore, the probability of rolling a 5 can be calculated as the number of ways the desired outcome can occur 1 out of the total number of possible outcomes 6 or:. The above example is the simplest form of probability calculation. There are many other types of events in probability and it is important to understand each type, as the calculation of their respective probabilities differs. A simple event is an event that has only one outcome. For example, when flipping a coin, the outcome of the coin landing on heads is an example of a simple event; the coin landing on tails is an example of another simple event. The probability of a simple event is calculated as:. A compound event is an event that includes two or more simple events. Flipping a coin twice and having it land on heads twice is an example of a compound event.

The probability of a coin landing on heads twice in a row is a compound probability that is computed as the product of the probabilities of the independent events, or: 0. Refer to the compound events page for more information on how to compute compound probabilities for different types of events. Independent events are events in which the outcome of one event is unaffected by the outcome of another event. Flipping a coin is an example of an independent event because on each flip of a fair coin, the probability of acquiring a heads or tails is equal.

Dependent events are events in which the outcome of an event is affected by the outcome of some other event. Since the probability in the subsequent trial is affected by an outcome in the first, this is an example of a dependent event. Mutually exclusive events are events that cannot occur at the same time. The outcome of heads or tails when flipping a coin are examples of mutually exclusive events. In a single flip of a coin, the coin can only land on heads or tails. If it lands on heads, it means that the coin did not land on tails and vice versa , since both cannot occur at the same time. The complement of an event, A, denoted A C , is comprised of all outcomes that are not contained in event A. For example, a fair six-sided die has the possible outcomes 1, 2, 3, 4, 5, and 6.

The probabilities of A and A C must therefore sum to 1. In other words:. Probabilities are calculated differently based on a number of factors, including the types of events involved. Below are three commonly used rules. Refer to the set theory page for more information on the notation used. The multiplication rule is used to find the probability of two events occurring at the same time. If A and B are dependent events, the probability of A and B occurring at the same time is:. where P B A is the conditional probability of event B occurring given that event A has already occurred. Two cards are drawn from a standard deck of 52 cards. Let A be the event that a king is chosen.

B is the event that another king is chosen given that the first card chosen is not replaced into the deck. Calculate the probability of A and B both occurring. Since one king must be removed in the first draw in order to draw 2 kings in a row, the number of kings and total cards in the deck is reduced by 1. Bayes rule or Bayes' theorem is a type of conditional probability that can be derived from the multiplication rule. The probability of event A occurring given that event B has already occurred can be determined as:. Statistics is a discipline that involves collecting, organizing, displaying, analyzing, interpreting, and presenting data.

It is widely used in scientific research, when considering social problems, and for industrial purposes, among many other applications. On a base level, it involves proper data collection through sampling when population data is not known or cannot be determined, designing and conducting experimental and observational studies, and formulating conclusions or re-designing the studies based on the data. Two distinct branches of statistics are descriptive statistics and inferential statistics. Descriptive statistics is the branch of statistics concerned with summarizing data, be it in graphical, tabular, or some other form.

A descriptive statistic is a summary statistic used to describe data. Examples of well-known descriptive statistics include the mean, median, and mode; these are classified as measures of central tendency and are one of the key types of descriptive statistics that provide information about a central or typical value in a probability distribution. Measures of variability are another classification of descriptive statistic; they describe the spread of the data how stretched or squeezed the distribution is and include statistics such as the standard deviation, variance, and more. In particular, the histogram and the curve fitted to it indicate a normal distribution , which is a commonly encountered probability distribution throughout statistics.

Many natural phenomena exhibit a normal distribution, giving way to inferential statistics, which allows us to make inferences about data based on their probability distributions as well as other factors. In the real world, it is often not possible, or highly impractical to collect large amounts of data from populations of interest. Ideally, we would be able to acquire all the data we need for a population and make informed decisions based on the descriptive statistics they provide. Realistically, since this is rarely feasible, we instead make inferences about populations as a whole based on samples of said populations and the use of statistical methods; this is the goal of inferential statistics.

For example, we may want to know the mean score on the AP Physics exam for all high school students in the United States. Because of the large scale, it would be both difficult and expensive to obtain the results of every single student in the US. In such a case, inferential statistics can be used to estimate the mean score by collecting samples from the population of high school students, then using the sample data to make inferences or predictions about the mean score of the population as a whole. When studying random phenomena, we may want to assess whether any observed differences can be attributed to some given input, or if the observed differences can be attributed fully to random chance.

This is another area in which inferential statistics can be used through the process of statistical hypothesis testing. There are many different types of statistical hypothesis tests that can be used depending on the conditions of the experiment. In general, the process involves a statement of no difference, referred to as the null hypothesis , and a comparison of what is observed to what we would expect based on this null hypothesis. Through use of statistical methods, we can then draw conclusions about the significance of observed data. Example What is the probability of rolling a 5 with a fair 6-sided die? Therefore, the probability of rolling a 5 can be calculated as the number of ways the desired outcome can occur 1 out of the total number of possible outcomes 6 or: There is approximately a Example Two cards are drawn from a standard deck of 52 cards.