BioInformatics at FSU - whose job is it and why it needs to be done.
... Consider a transmitter T and a receiver R connected by one of Shannon's communication channels. T must transmit some data D to R. T and R may have previously agreed on a code book for hypotheses, using common knowledge and prior expectations. If T can find a good hypothesis, H, (theory, structure, ...
... Consider a transmitter T and a receiver R connected by one of Shannon's communication channels. T must transmit some data D to R. T and R may have previously agreed on a code book for hypotheses, using common knowledge and prior expectations. If T can find a good hypothesis, H, (theory, structure, ...
The Distribution of Order Statistics for Discrete Random Variables
... large amount of literature has been devoted to the theory and application of order statistics. In conjunction, a growing interest in undergraduate and graduate courses in order statistics (Arnold et al. 1992) has also emerged over the past ten years. Many popular mathematical statistics texts, such ...
... large amount of literature has been devoted to the theory and application of order statistics. In conjunction, a growing interest in undergraduate and graduate courses in order statistics (Arnold et al. 1992) has also emerged over the past ten years. Many popular mathematical statistics texts, such ...
h - WSU EECS
... Log terms can be viewed as (negative of) bits to encode data given hypothesis + bits to encode hypothesis This is the basic idea of minimum description length (MDL) learning For deterministic hypotheses, P (d|hi) is 1 if consistent, 0 otherwise ⇒ MAP = simplest consistent hypothesis (cf. science) ...
... Log terms can be viewed as (negative of) bits to encode data given hypothesis + bits to encode hypothesis This is the basic idea of minimum description length (MDL) learning For deterministic hypotheses, P (d|hi) is 1 if consistent, 0 otherwise ⇒ MAP = simplest consistent hypothesis (cf. science) ...
PROBABILITY - Spokane Public Schools
... Golf balls must meet a set of five standards in order to be used in professional tournaments. One of these standards is distance traveled. When a ball is hit by a mechanical device, Iron Byron, with a 10-degree angle of launch, a backspin of 42 revolutions per second, and a ball velocity of 235 feet ...
... Golf balls must meet a set of five standards in order to be used in professional tournaments. One of these standards is distance traveled. When a ball is hit by a mechanical device, Iron Byron, with a 10-degree angle of launch, a backspin of 42 revolutions per second, and a ball velocity of 235 feet ...
Solutions #7 - Bryn Mawr College
... (1) If W = X + Y, then E(W) = E(X) + E(Y) always, provided only that E(X) and E(Y) exist. This is true regardless of what X and Y are, or how they are related. We’ll prove this. (2) If U = YZ, then E(U) may or may not be the same as E(Y)E(Z). We will discover when these numbers are equal. When they ...
... (1) If W = X + Y, then E(W) = E(X) + E(Y) always, provided only that E(X) and E(Y) exist. This is true regardless of what X and Y are, or how they are related. We’ll prove this. (2) If U = YZ, then E(U) may or may not be the same as E(Y)E(Z). We will discover when these numbers are equal. When they ...
Mathematics Strand 1 Sample Questions Higher and Ordinary Level
... The company is considering switching brands from Evertread tyres to SafeRun tyres, because they are cheaper. The distributors of SafeRun tyres claim that these tyres have the same mean lifespan as Evertread tyres. The car rental company wants to check this claim before they switch brands. They have ...
... The company is considering switching brands from Evertread tyres to SafeRun tyres, because they are cheaper. The distributors of SafeRun tyres claim that these tyres have the same mean lifespan as Evertread tyres. The car rental company wants to check this claim before they switch brands. They have ...
Slide 1
... interest is more important than the assumption that the two population distributions are Normal. Small sample sizes (n1 + n2 < 15): Use t procedures if each data set appears close to Normal (symmetric, single peak, no outliers). If a data set is skewed or if outliers are present, do not use t. Mediu ...
... interest is more important than the assumption that the two population distributions are Normal. Small sample sizes (n1 + n2 < 15): Use t procedures if each data set appears close to Normal (symmetric, single peak, no outliers). If a data set is skewed or if outliers are present, do not use t. Mediu ...
I N S T I T U T D E
... analysis. This has a potential to interfere with the performance of two-sample statistical tests, since the use of different tuning parameters for the smoothing step, or different observation times or subsample sizes (i.e. numbers of observations per curve), can mask the differences between distribu ...
... analysis. This has a potential to interfere with the performance of two-sample statistical tests, since the use of different tuning parameters for the smoothing step, or different observation times or subsample sizes (i.e. numbers of observations per curve), can mask the differences between distribu ...
p(E|S)
... • Definition 1: Suppose that S is a set with n elements. The uniform distribution assigns the probability 1/n to each element of S. • Definition 2: The probability of the event E is the sum of the probabilities of the outcomes in E. That is, p(E)= sEp(s) – Selecting at random – Ex.2 ...
... • Definition 1: Suppose that S is a set with n elements. The uniform distribution assigns the probability 1/n to each element of S. • Definition 2: The probability of the event E is the sum of the probabilities of the outcomes in E. That is, p(E)= sEp(s) – Selecting at random – Ex.2 ...
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.