Notes in statistics and stochastics

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Status	Last Update	Fields
Published	06/25/2024	How is Chebyshev's inequality represented mathematically?
Published	06/25/2024	What is the study of how to use information to guide action in practical situations involving uncertainty?
Published	06/25/2024	Give examples of uncertain situations mentioned in the text.
Published	06/25/2024	What defines uncertainty?
Published	06/25/2024	What is probabilistic modelling made of?
Published	06/25/2024	How is a model described in the text?
Published	06/25/2024	What are the steps of statistical modelling mentioned?
Published	06/25/2024	What is deductive/probabilistic configuration focused on?
Published	06/25/2024	What characterizes inductive/statistic configuration?
Published	06/25/2024	What is stochastics?
Published	06/25/2024	How does stochastics differ from statistics?
Published	06/25/2024	What is the certain event that occurs in every trial?
Published	06/25/2024	What does the set function Prob{E} assign to each event E?
Published	06/25/2024	What follows from having disjoint events A1, A2, A3, ...?
Published	06/25/2024	How is the probability of event E calculated in a random experiment?
Published	06/25/2024	What are the characteristics of a random experiment?
Published	06/25/2024	What is a sample space in the context of random experiments?
Published	06/25/2024	What does the symbol Ω represent in a sample space?
Published	06/25/2024	What does it mean for events to be disjoint or mutually exclusive?
Published	06/25/2024	What visualization tool is commonly used in probability?
Published	06/25/2024	What is conditional probability?
Published	06/25/2024	How is the probability of the union of events calculated given event E1?
Published	06/25/2024	What is the relationship between conditional probability and events?
Published	06/25/2024	What does an odds ratio greater than 1 indicate?
Published	06/25/2024	What is Bayes' theorem?
Published	06/25/2024	What are joint probabilities?
Published	06/25/2024	What is the purpose of marginal probabilities?
Published	06/25/2024	What is an array of joint/marginal joint probabilities used for?
Published	06/25/2024	How is the number of elements in a sample space calculated?
Published	06/25/2024	What does it mean for events to be mutually exclusive?
Published	06/25/2024	What is a trial in the context of random experiments?
Published	06/25/2024	How is the sample space of a combined random experiment calculated?
Published	06/25/2024	What does the Principle of Indifference state?
Published	06/25/2024	What is the principle of the Frequentist interpretation of probability?
Published	06/25/2024	What does the Weak Law of Large Numbers (WLLN) state?
Published	06/25/2024	What is the interpretation of probability in the Bayesian approach?
Published	06/25/2024	Are direct and inverse conditional probabilities the same?
Published	06/25/2024	How is the odds ratio defined in terms of probability?
Published	06/25/2024	What does an odds ratio less than 1 indicate?
Published	06/25/2024	What are marginal probabilities?
Published	06/25/2024	What is the sum of all probabilities in a sample space?
Published	06/25/2024	What are quantitative variables characterized by?
Published	06/25/2024	Is a discrete variable countable?
Published	06/25/2024	Does a continuous variable have finite possibilities?
Published	06/25/2024	What is an example of a discrete variable?
Published	06/25/2024	What type of variable is weight?
Published	06/25/2024	What are qualitative variables also known as?
Published	06/25/2024	What are the two types of qualitative variables mentioned?
Published	06/25/2024	What is a random variable z according to the text?
Published	06/25/2024	What is the probability function associated with discrete random variables?
Published	06/25/2024	What are continuous random variables defined as?
Published	06/25/2024	What does Chebyshev's inequality guarantee?
Published	06/25/2024	Are qualitative variables countable?
Published	06/25/2024	Do continuous variables have finite possibilities?
Published	06/25/2024	What is an example of a qualitative variable?
Published	06/25/2024	What are the types of qualitative variables mentioned?
Published	06/25/2024	What is a random variable z defined as in the text?
Published	06/25/2024	What are the conditions for a random variable z to be fulfilled?
Published	06/25/2024	What are random variables in the context of uncertain events or experiments?
Published	06/25/2024	What is entropy a measure of in relation to random variables?
Published	06/25/2024	What are discrete random variables defined as?
Published	06/25/2024	What is the cumulative distribution function for continuous random variables?
Published	06/25/2024	What is independence between two events A and B defined as?
Published	06/25/2024	What does a distribution characterize in an experiment?
Published	06/25/2024	What is a family of probability distributions?
Published	06/25/2024	What are moments in the context of distributions?
Published	06/25/2024	What are central moments, and how are they calculated?
Published	06/25/2024	What is skewness, and what does it measure?
Published	06/25/2024	How is skewness interpreted in different distributions?
Published	06/25/2024	What is kurtosis, and what does it measure?
Published	06/25/2024	How is kurtosis interpreted in different distributions?
Published	06/25/2024	What does the central limit theorem state?
Published	06/25/2024	What is a Bernoulli trial?
Published	06/25/2024	What type of random variable is associated with a Bernoulli trial?
Published	06/25/2024	What is a cumulative distribution function (CDF)?
Published	06/25/2024	What is a probability density function (PDF)?
Published	06/25/2024	What type of distributions are described by PDFs?
Published	06/25/2024	What is the expectation value in the context of a PDF?
Published	06/25/2024	What is the variance in the context of a PDF?
Published	06/25/2024	What are probability mass functions (PMFs) used for?
Published	06/25/2024	What is the combination involved in a probability mass function?
Published	06/25/2024	What is the first power associated with in moments?
Published	06/25/2024	What is the second power associated with in moments?
Published	06/25/2024	What does the third power in moments measure?
Published	06/25/2024	What is the fourth power in moments associated with?
Published	06/25/2024	What is a binomial distribution?
Published	06/25/2024	What is the random variable associated with a binomial distribution?
Published	06/25/2024	What is the mean of a binomial distribution?
Published	06/25/2024	What is the variance of a binomial distribution?
Published	06/25/2024	What is a special case of the binomial distribution?
Published	06/25/2024	What characterizes the distribution of a binomial distribution?
Published	06/25/2024	What is a geometrical distribution?
Published	06/25/2024	What is the probability mass function for X in a geometrical distribution?
Published	06/25/2024	What is the probability mass function for Y in a geometrical distribution?
Published	06/25/2024	What is a continuous distribution?
Published	06/25/2024	What is a Poisson distribution?
Published	06/25/2024	What is the probability mass function for a Poisson distribution?
Published	06/25/2024	What is a uniform distribution?
Published	06/25/2024	What is the expected value of a uniform distribution?
Published	06/25/2024	What is a gamma distribution?
Published	06/25/2024	What is a special case of the gamma distribution?
Published	06/25/2024	What are key properties of the normal distribution?
Published	06/25/2024	What is the standard normal distribution?
Published	06/25/2024	How are z-scores calculated in the standard normal distribution?
Published	06/25/2024	What is the purpose of standardizing a normal distribution?
Published	06/25/2024	What is covariance?
Published	06/25/2024	How is covariance calculated?
Published	06/25/2024	What does a positive covariance indicate?
Published	06/25/2024	What does a negative covariance indicate?
Published	06/25/2024	What does a covariance of zero indicate?
Published	06/25/2024	What are the limitations of covariance?
Published	06/25/2024	How is covariance normalized?
Published	06/25/2024	What is correlation?
Published	06/25/2024	What are the types of correlation?
Published	06/25/2024	What is linear correlation?
Published	06/25/2024	What is non-linear correlation?
Published	06/25/2024	What is rank correlation?
Published	06/25/2024	What is the Spearman's rank correlation coefficient?
Published	06/25/2024	What is an important note regarding correlation and causation?
Published	06/25/2024	What is an important consideration about the strength of a correlation coefficient?
Published	06/25/2024	What does the term "sample" denote?
Published	06/25/2024	What are the characteristics of the distribution of a sample?
Published	06/25/2024	Why do statisticians use estimation methodologies?
Published	06/25/2024	What does parametric estimation involve in statistics?
Published	06/25/2024	What are the two main approaches to parametric estimation?
Published	06/25/2024	In Bayesian estimation, what are the parameters considered?
Published	06/25/2024	What is the first step in the procedure of Bayesian estimation?
Published	06/25/2024	What is the goal of Bayesian estimation?
Published	06/25/2024	What is the outcome of point estimation?
Published	06/25/2024	What is a confidence interval?
Published	06/25/2024	What is the Plug-in principle in estimation methodology?
Published	06/25/2024	How is the population mean estimated using the Plug-in principle?
Published	06/25/2024	What is maximum likelihood estimation based on?
Published	06/25/2024	What is a sampling distribution in statistics?
Published	06/25/2024	How does the accuracy of 𝜃̄ increase with more samples?
Published	06/25/2024	How is the standard error calculated?
Published	06/25/2024	When is an estimator considered unbiased?
Published	06/25/2024	What is the bias of an estimator?
Published	06/25/2024	What does the variance of an estimator represent?
Published	06/25/2024	What is the variance of the sample mean?
Published	06/25/2024	How is the accuracy of a sample mean indicated?
Published	06/25/2024	What is the main idea behind maximum likelihood estimation?
Published	06/25/2024	What does the standard error represent in statistics?
Published	06/25/2024	What is the expected value of the sample mean?
Published	06/25/2024	How does the standard error relate to the accuracy of the sample mean?
Published	06/25/2024	What does the variance of an estimator indicate?
Published	06/25/2024	How is the standard error calculated from the variance?
Published	06/25/2024	What is the primary purpose of estimation in statistics?
Published	06/25/2024	What does parametric estimation involve?
Published	06/25/2024	What distinguishes frequentist/classical approach from Bayesian approach in estimation?
Published	06/25/2024	What does a confidence interval represent?
Published	06/25/2024	What is the Plug-in principle used for in estimation?
Published	06/25/2024	what is the degree of freedom?
Published	06/25/2024	how is the degree of freedom calculated?
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