Lecture 3. Conditional probability . Discrete and continuous random
... Let’s return to the first example considered in the beginning of the lecture: You flip a fair coin 10 times and count the number of heads X. How could we describe the rule to define the probabilities of possible values of X? That’s the classical example of a random variable having binomial probabili ...
... Let’s return to the first example considered in the beginning of the lecture: You flip a fair coin 10 times and count the number of heads X. How could we describe the rule to define the probabilities of possible values of X? That’s the classical example of a random variable having binomial probabili ...
Basic Concepts of Discrete Probability
... Probability Measure • Let us consider an event of interest A as the set of outcomes ak. • Let a real function m(ak ) be the probability measure of the outcome ak. • The probability measure of an event is defined as the sum of the probability measures associated with all the outcomes ak of that even ...
... Probability Measure • Let us consider an event of interest A as the set of outcomes ak. • Let a real function m(ak ) be the probability measure of the outcome ak. • The probability measure of an event is defined as the sum of the probability measures associated with all the outcomes ak of that even ...
Testing the Validity of a Demand Model: An Operations Perspective
... Prescriptive solutions to applied problems in operations management invariably hinge on the specification of a model for the underlying system or phenomenon of interest. The key model primitives (e.g., demand distribution, service time distribution, functional relationships between decision variable ...
... Prescriptive solutions to applied problems in operations management invariably hinge on the specification of a model for the underlying system or phenomenon of interest. The key model primitives (e.g., demand distribution, service time distribution, functional relationships between decision variable ...
applied mathematics syllabus
... must, on registering these candidates at the start of the qualifying year, have them confirm in the required form, the Associate Degree they wish to be awarded. Candidates will not be awarded any possible alternatives for which they ...
... must, on registering these candidates at the start of the qualifying year, have them confirm in the required form, the Associate Degree they wish to be awarded. Candidates will not be awarded any possible alternatives for which they ...
NOTE C: GUIDE TO EXCEL STATISTICAL FUNCTIONS AND TOOLS
... FISHER – Returns the Fisher transformation of a correlation coefficient (close to 1) that approximates normal distribution z values. FISHERINV – Returns a correlation coefficient, which is the inverse of the Fisher transformation, given a z value. GAMMALN – Returns the natural logarithm of the gamma ...
... FISHER – Returns the Fisher transformation of a correlation coefficient (close to 1) that approximates normal distribution z values. FISHERINV – Returns a correlation coefficient, which is the inverse of the Fisher transformation, given a z value. GAMMALN – Returns the natural logarithm of the gamma ...
P - OSU Physics
... If we look at the three choices for the coin flip example, each term is of the form: CmpmqN-m m = 0, 1, 2, N = 2 for our example, q = 1 - p always! coefficient Cm takes into account the number of ways an outcome can occur without regard to order. for m = 0 or 2 there is only one way for the outcome ...
... If we look at the three choices for the coin flip example, each term is of the form: CmpmqN-m m = 0, 1, 2, N = 2 for our example, q = 1 - p always! coefficient Cm takes into account the number of ways an outcome can occur without regard to order. for m = 0 or 2 there is only one way for the outcome ...
Belief Propagation algorithm in Markov Random Fields
... new URLs, what is the probability that s/he will arrive at a given page? The PageRank of a page captures this notion More “popular” or “worthwhile” pages get a higher rank This gives a rule for random walk on The Web graph (a directed graph). ...
... new URLs, what is the probability that s/he will arrive at a given page? The PageRank of a page captures this notion More “popular” or “worthwhile” pages get a higher rank This gives a rule for random walk on The Web graph (a directed graph). ...
Joint Distribution of Minimum of N Iid Exponential Random Variables
... properties of this vector such as PDF, CDF and stochastic representations. Our results include explicit formulas for marginal and conditional distributions, moments and moments generating functions. We also derive moments estimators and maximum likelihood estimators of the parameter of this distribu ...
... properties of this vector such as PDF, CDF and stochastic representations. Our results include explicit formulas for marginal and conditional distributions, moments and moments generating functions. We also derive moments estimators and maximum likelihood estimators of the parameter of this distribu ...
![P(N[2])+ - Brandeis](http://s1.studyres.com/store/data/002585646_1-3672ee18c60f46639358706fc75d7a0e-300x300.png)
P(N[2])+ - Brandeis
... analyst). Then, the probability that he voted for his opponent, P(Bc) = 0.55. •Suppose now that some voters are reluctant to answer the questions. Let A = “The voter stops and answers a question about how she voted”, and suppose that P(A|B)=0.4 and P(A|Bc)=0.3. That is, 40% of Bradley’s voters will ...
... analyst). Then, the probability that he voted for his opponent, P(Bc) = 0.55. •Suppose now that some voters are reluctant to answer the questions. Let A = “The voter stops and answers a question about how she voted”, and suppose that P(A|B)=0.4 and P(A|Bc)=0.3. That is, 40% of Bradley’s voters will ...
Chapter 5 - Probability
... Probability is a numerical measure of the likelihood that a specific event will occur. If A denotes an event, the probability for the event A is denoted P(A). People often have some idea of what probability means, and they often think of it in percentages. In statistics we tend to not use percent no ...
... Probability is a numerical measure of the likelihood that a specific event will occur. If A denotes an event, the probability for the event A is denoted P(A). People often have some idea of what probability means, and they often think of it in percentages. In statistics we tend to not use percent no ...
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.