Statistics in geophysics introduction and probability theory

... 1000 1500 Days since January 1st, 2002 Winter Term 2013/14 7/32 2000 Introduction Probability Theory Course outline Probability Theory Descriptive Statistics Inferential Statistics Linear Regression ... 27/32 Introduction Probability Theory Set theory The meaning of probability Some properties of the probability function Multiplicative law of probability and inde...

Ngày tải lên: 04/12/2015, 17:09

... heads obtained in the three tosses ω X (ω) HHH HHT HTH THH TTH THT HTT TTT Table: Enumeration of the value of X for each point in the sample space x P(X = x) 1/8 3/8 3/8 1/8 Table: Induced probability ... distribution describes the number of events occurring in a certain time interval and so pertains to data on counts A random variable X is defined to have a Poisson distribution, deno...

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... The main purpose of this paper is to show that many inequalities in functional analysis, probability theory and combinatorics are immediate corollaries of (2) ... Caen-Selberg inequality to the study of the finite field Kakeya and Nikodym problems in classical analysis the electronic journal of combinatorics 17 (2010), #R58 2 Inequalities in Functional Analysis ... Nikodym...

Ngày tải lên: 08/08/2014, 12:22

... were removed in the Cantor set construction of Example 3.2  CHAPTER Introduction to Probability Theory 35 In addition to tossing a coin, another common random experiment is to pick a number, perhaps ... X and the probability measure IP we use in If we set the probability of H to be , then LS2 assigns mass to the number 16 If we set the probability of H to be , then LS...

Ngày tải lên: 18/10/2013, 03:20

... (x)p(x)dx = Ef with the Riemann-integral on the left-hand side and the expectation of the random variable f with respect to the probability space (R, B(R), P) on the right-hand side Let us consider ... L and An ⊆ An+ 1 , n = 1, 2, imply ∞ n=1 An ∈ L Proposition 1.4.2 [ - -Theorem] If P is a π-system and L is a λsystem, then P ⊆ L implies σ(P) ⊆ L Definition 1.4.3 [equivalence relati...

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Ngày tải lên: 08/04/2014, 12:21

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Ngày tải lên: 08/04/2014, 12:21

... −1 ≤ rSP ≤ Interpretation: rSP > 0: Y tends to increase when X increases rSP < 0: Y tends to decrease when X increases rSP = 0: No tendency for Y to either increase or decrease when X increases ... modified version The following quantities (called fences) can be used for identifying extreme values in the tails of the distribution: lower inner fence: x0.25 − 1.5 × IQR; upper inner fence: x0....

Ngày tải lên: 04/12/2015, 17:07

... statistical ideas is in making sense of a set of data The goal is to extract insights about the processes underlying the generation of the numbers Descriptive statistics is the discipline of quantitatively ... finite or countable set of different values continuous: uncountable set of different values quasi-continuous: data are continuous but measured in a discrete way Winter Term 2013...

Ngày tải lên: 04/12/2015, 17:07

... Generalized linear models Binary regression Count data regression Components of the classical linear model Generalized linear models (GLMs) are an extension of classical linear models ... substituted into the respective model and the total number of parameters should be increased to p + Winter Term 2013/14 13/25 Generalized linear models Binary regression Count data reg...

Ngày tải lên: 04/12/2015, 17:08

... distribution-free) tests Winter Term 2013/14 2/27 Introduction to hypothesis testing Some commonly encountered parametric tests Sampling distribution The sampling distribution for a statistic (including the test ... it justify questioning, the claim? This problem fits neatly into the parametric setting of the binomial distribution Winter Term 2013/14 11/27 Introduction to hypothesis testing S...

Ngày tải lên: 04/12/2015, 17:08

... Paired samples Two independent samples Background Tests not requiring assumptions involving specific parametric distributions for the data or for the sampling distribution of the test statistics are ... X1 , , Xn , Y1 , , Ym in ascending order Define Vi = if the i-th order statistic belongs to the X sample if the i-th order statistic belongs to the Y sample Winter Term 2013/14 9/10 Nonpar...

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... defined by summing the arguments and then dividing by n Winter Term 2013/14 3/26 Estimation by Maximum Likelihood Properties of Estimators Confidence Intervals Background In 1921, R A Fisher pointed ... parameters Winter Term 2013/14 12/26 Estimation by Maximum Likelihood Properties of Estimators Confidence Intervals Evaluating estimators We have outlined reasonable techniques for finding o...

Ngày tải lên: 04/12/2015, 17:09

... nonlinear relationships between continuous covariates and the response within the scope of linear models Two simple methods for dealing with nonlinearity: Variable transformation; Polynomial regression ... 13.8 25 W Turkey weights in pounds, ages in weeks, and origin (Georgia (G); Virgina (V); Wisconsin (W)), of 13 Thanksgiving turkeys Winter Term 2013/14 6/28 Multiple linear regre...

Ngày tải lên: 04/12/2015, 17:09