QUANTILE OPTIMIZATION FOR HEAVY
... environment, optimizing the quantile is a robust procedure, and almost always a reasonable thing to do in a complex, volatile, and heavy-tailed environment or in a situation where the worst-case scenario is unknown or too extreme. For the past decade, many countries have deregulated their electricit ...
... environment, optimizing the quantile is a robust procedure, and almost always a reasonable thing to do in a complex, volatile, and heavy-tailed environment or in a situation where the worst-case scenario is unknown or too extreme. For the past decade, many countries have deregulated their electricit ...
23 Binomial Problems
... There are 15 trials each with 2 outcomes. Since the students were chosen at random, the trials are independent. However, the probability of a student travelling by bus is not constant. For example, some will be close enough to walk and others will be close to a train station, making the probability ...
... There are 15 trials each with 2 outcomes. Since the students were chosen at random, the trials are independent. However, the probability of a student travelling by bus is not constant. For example, some will be close enough to walk and others will be close to a train station, making the probability ...
REPEATED TRIALS
... We first note a basic fact about probability and counting. Suppose E1 and E2 are independent events. For example, you could think of E1 as the event of tossing two dice and getting a sum of 7. You could think of E2 as the event of tossing two dice and getting a sum of 12. Now ask the question: What ...
... We first note a basic fact about probability and counting. Suppose E1 and E2 are independent events. For example, you could think of E1 as the event of tossing two dice and getting a sum of 7. You could think of E2 as the event of tossing two dice and getting a sum of 12. Now ask the question: What ...
Statistical methods for DNA copy-number detection
... (SNPs) have been used to assess DNA copy-number in the studied genome. Since this approach is regularly used in parallel with array-CGH, it is often referred to as SNPCGH. The advantage of a combined SNP-CGH approach is the identification of allele specific gain and loss by SNP array and the robust ...
... (SNPs) have been used to assess DNA copy-number in the studied genome. Since this approach is regularly used in parallel with array-CGH, it is often referred to as SNPCGH. The advantage of a combined SNP-CGH approach is the identification of allele specific gain and loss by SNP array and the robust ...
Document
... • Identify a random variable as geometric by verifying four conditions: two outcomes (success and failure); independent trials; the same probability of success for each trial; and the count of interest is the number of trials required to get the first success. • Use formulas or technology to determi ...
... • Identify a random variable as geometric by verifying four conditions: two outcomes (success and failure); independent trials; the same probability of success for each trial; and the count of interest is the number of trials required to get the first success. • Use formulas or technology to determi ...
Statistics
Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, e.g., a scientific, industrial, or societal problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as ""all persons living in a country"" or ""every atom composing a crystal"". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.Two main statistical methodologies are used in data analysis: descriptive statistics, which summarizes data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draws conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena.A standard statistical procedure involves the test of the relationship between two statistical data sets, or a data set and a synthetic data drawn from idealized model. An hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a ""false positive"") and Type II errors (null hypothesis fails to be rejected and an actual difference between populations is missed giving a ""false negative""). Multiple problems have come to be associated with this framework: ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis.Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other important types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of missing data and/or censoring may result in biased estimates and specific techniques have been developed to address these problems.Statistics can be said to have begun in ancient civilization, going back at least to the 5th century BC, but it was not until the 18th century that it started to draw more heavily from calculus and probability theory. Statistics continues to be an area of active research, for example on the problem of how to analyze Big data.