Revised_NonCompacting7th_Grade_Math_Curriculum_Guide
... two populations. Investigate chance processes and develop, use, and evaluate probability models. Clarifying Objectives ...
... two populations. Investigate chance processes and develop, use, and evaluate probability models. Clarifying Objectives ...
Random variables, probability distributions, binomial
... X =X HTT =2 counts the number of tails in the three coin flips. example with =HTT , A discrete random variable is one which only takes a finite or countable set of values as opposed to a continuous random variable which can take say any real number value in an interval of real numbers. (Ther ...
... X =X HTT =2 counts the number of tails in the three coin flips. example with =HTT , A discrete random variable is one which only takes a finite or countable set of values as opposed to a continuous random variable which can take say any real number value in an interval of real numbers. (Ther ...
Unit 4 The Bernoulli and Binomial Distributions
... • The random variable X is the “winnings”. Recall that this variable has possible values x=$1, $5, $10, and $25. • The statistical expectation of X is μ = $5.75. Recall that this figure is what the state of Massachusetts can expect to pay out, on average, in the long run. • What about the variabilit ...
... • The random variable X is the “winnings”. Recall that this variable has possible values x=$1, $5, $10, and $25. • The statistical expectation of X is μ = $5.75. Recall that this figure is what the state of Massachusetts can expect to pay out, on average, in the long run. • What about the variabilit ...
Spring 2014
... Suppose that is continuously distributed with support and that the only objects that are observed are the density of and Pr ( ≥ 0| = ) for all in the support of Determine what functions and parameters can be identified from these observed objects. If a function or parameter is not iden ...
... Suppose that is continuously distributed with support and that the only objects that are observed are the density of and Pr ( ≥ 0| = ) for all in the support of Determine what functions and parameters can be identified from these observed objects. If a function or parameter is not iden ...
Chapter 6
... 3. Simulate many repetitions. 4. State your conclusions – note what is to be counted (what is the purpose of the simulation), and give the count if requested. DO NOT say “proves” or “definitely true” – say “sufficient evidence to support” your claim Def: Each time we obtain a simulated answer to our ...
... 3. Simulate many repetitions. 4. State your conclusions – note what is to be counted (what is the purpose of the simulation), and give the count if requested. DO NOT say “proves” or “definitely true” – say “sufficient evidence to support” your claim Def: Each time we obtain a simulated answer to our ...
Probability Probability is the study of uncertain events or outcomes
... In each of these situations, the result is uncertain. We will not actually know the result until after we collect the data. In all of these situations, we can use probability models to describe the patterns of variation we are likely to see. Experiments, Trials, Outcomes, Sample Spaces Consider some ...
... In each of these situations, the result is uncertain. We will not actually know the result until after we collect the data. In all of these situations, we can use probability models to describe the patterns of variation we are likely to see. Experiments, Trials, Outcomes, Sample Spaces Consider some ...
Unit 2: Modeling Random Behavior Week 3 : Probability
... A Nickel–Hydrogen battery (NiH2 or Ni–H2) is a rechargeable electrochemical power source based on Nickel and Hydrogen. It differs from a Nickel–metal hydride (NIMH) battery by the use of hydrogen in a pressurized cell at up to 8.5 MPa. The screen shot below gives more details on the structure of thi ...
... A Nickel–Hydrogen battery (NiH2 or Ni–H2) is a rechargeable electrochemical power source based on Nickel and Hydrogen. It differs from a Nickel–metal hydride (NIMH) battery by the use of hydrogen in a pressurized cell at up to 8.5 MPa. The screen shot below gives more details on the structure of thi ...
New Explicit Expressions for Relative Frequencies of
... (SNP) frequencies in populations with time-varying size. Our approach is based on deriving analytical expressions for frequencies of SNPs. Analytical expressions allow for computations that are faster and more accurate than Monte Carlo simulations. In contrast to other articles showing analytical fo ...
... (SNP) frequencies in populations with time-varying size. Our approach is based on deriving analytical expressions for frequencies of SNPs. Analytical expressions allow for computations that are faster and more accurate than Monte Carlo simulations. In contrast to other articles showing analytical fo ...
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.