The expectations hypothesis of the term structure of interest rates (whose graphical representation is known as the yield curve) is the proposition that the long-term rate is determined purely by current and future expected short-term rates, in such a way that the expected final value of wealth from investing in a sequence of short-term bonds equals the final value of wealth from investing in long-term bonds. This hypothesis assumes that the various maturities are perfect substitutes and suggests that the shape of the yield curve depends on market participants' expectations of future interest rates. These expected rates, along with an assumption that arbitrage opportunities will be minimal, is enough information to construct a complete yield curve. For example, if investors have an expectation of what 1-year interest rates will be next year, the 2-year interest rate can be calculated as the compounding of this year's interest rate by next year's interest rate. More generally, returns (1 + yield) on a long-term instrument are equal to the geometric mean of the returns on a series of short-term instruments, as given by where lt and st respectively refer to long-term and short-term bonds, and where interest rates i for future years are expected values.This theory is consistent with the observation that yields usually move together. However, it fails to explain the persistence in the non-horizontal shape of the yield curve. (Wikipedia).
(PP 4.1) Expectation for discrete random variables
(0:00) Definition of expectation for discrete r.v.s. (4:17) Well-defined expectation. (8:15) E(X) may exist and be infinite. (10:58) E(X) might fail to exist. A playlist of the Probability Primer series is available here: http://www.youtube.com/view_play_list?p=17567A1A3F5DB5E4
From playlist Probability Theory
Expectation Values in Quantum Mechanics
Expectation values in quantum mechanics are an important tool, which help us to mathematically describe measurements of quantum systems. You can think of expectation values as the average of all possible outcomes of a measurement, weighted by their respective probabilities. Contents: 00:
From playlist Quantum Mechanics, Quantum Field Theory
(0:00) Function of a random variable is a random variable. (1:43) Expectation rule. A playlist of the Probability Primer series is available here: http://www.youtube.com/view_play_list?p=17567A1A3F5DB5E4
From playlist Probability Theory
Introduction to Estimation Theory
http://AllSignalProcessing.com for more great signal-processing content: ad-free videos, concept/screenshot files, quizzes, MATLAB and data files. General notion of estimating a parameter and measures of estimation quality including bias, variance, and mean-squared error.
From playlist Estimation and Detection Theory
(PP 4.2) Expectation for random variables with densities
(0:00) Definition of expectation for r.v.s. with densities. (2:30) E(X) for a uniform random variable. (5:05) Well-defined expectation. (7:15) E(X) may exist and be infinite. (8:00) E(X) might fail to exist. A playlist of the Probability Primer series is available here: http://www.youtub
From playlist Probability Theory
What is a hypothesis test? The meaning of the null and alternate hypothesis, with examples. Overview of test statistics and confidence levels.
From playlist Hypothesis Tests and Critical Values
From playlist STAT 501
Teach Astronomy - Testing a Hypothesis
http://www.teachastronomy.com/ One of the basic tasks of science is to test hypotheses. A hypothesis is a description of a set of data, a model, usually a mathematical description in most branches of science. To test a hypothesis we need data of sufficient quantity and quality, and our a
From playlist 01. Fundamentals of Science and Astronomy
What Is The Uncertainty Principle?
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From playlist Science Unplugged: Quantum Mechanics
Chapter 11.1: Chi-Squared Test for Goodness of Fit
Chapter 11.1 from "Introduction to Statistics, Think & Do" by Scott Stevens (http://www.StevensStats.com) Textbook from Publisher, $29.95 print, $9.95 PDF http://www.centerofmathematics.com/wwcomstore/index.php/thinkdov4-1.html Textbook from Amazon: https://amzn.to/2zJRCjL
From playlist Statistics Lecture Videos
MIT RES.TLL-004 Concept Vignettes View the complete course: http://ocw.mit.edu/RES-TLL-004F13 Instructor: Lourdes Aleman In this video, students will learn how to apply Chi square hypothesis testing to experimental data obtained from genetic experiments. License: Creative Commons BY-NC-S
From playlist MIT STEM Concept Videos
Statistics: Ch 9 Hypothesis Testing (3 of 35) What is the "Null Hypothesis"?
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 The alternative hypothesis gives a different (or alternate) explanation about the product, the design, of the capability that indicat
From playlist STATISTICS CH 9 HYPOTHESIS TESTING
Statistical Learning: Introduction to Hypothesis Testing
Statistical Learning, featuring Deep Learning, Survival Analysis and Multiple Testing You are able to take Statistical Learning as an online course on EdX, and you are able to choose a verified path and get a certificate for its completion: https://www.edx.org/course/statistical-learning
From playlist Statistical Learning
Lecture 08 - Bias-Variance Tradeoff
Bias-Variance Tradeoff - Breaking down the learning performance into competing quantities. The learning curves. Lecture 8 of 18 of Caltech's Machine Learning Course - CS 156 by Professor Yaser Abu-Mostafa. View course materials in iTunes U Course App - https://itunes.apple.com/us/course/ma
From playlist Machine Learning Course - CS 156
0:55 - Review #1: Frequency tables 1:27 - Review #2: Two-way contingency tables 2:24 - Review #3: Probability distribution plots 3:26 - Review #4: Conditional probabilities 5:14 - Review #5: Independence 6:08 - Lesson 11 learning objectives 6:38 - 1. Construct a chi-square probability dist
From playlist STAT 200 Video Lectures
Simple Linear Regression (Part C)
Regression Analysis by Dr. Soumen Maity,Department of Mathematics,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Kharagpur: Regression Analysis | CosmoLearning.org Mathematics
Hypothesis testing (ALL YOU NEED TO KNOW!)
0:00 Introduction 3:41 Intuition behind hypothesis testing 10:16 Example 1 12:57 Null hypothesis 22:00 Test statistic 28:27 p-valiue 33:38 Confidence intervals 37:46 Significant treatment difference 42:25 Power and Sample size (THE BEST!) 50:47 Example 2
From playlist Statistical Inference (7 videos)
Chi-squared Goodness of Fit Test! Extensive video!
See all my videos at https://www.zstatistics.com/ 0:42 INTRODUCTION 3:40 EXAMPLE 1 - Formal goodness of fit test (1 df) 17:02 ADVANCED - Where is the normal distribution hiding?? 22:56 EXAMPLE 2 - Formal goodness of fit test (2 df) Formula proof: It actually exists neatly on the wikipedi
From playlist Hypothesis testing
Statistical Analysis And Business Applications | Data Science With Python Tutorial
🔥 Advanced Certificate Program In Data Science: https://www.simplilearn.com/pgp-data-science-certification-bootcamp-program?utm_campaign=StatisticalAnalysis-kEN-YsAkEMs&utm_medium=Descriptionff&utm_source=youtube 🔥 Data Science Bootcamp (US Only): https://www.simplilearn.com/data-science-b
Introduction to Detection Theory (Hypothesis Testing)
http://AllSignalProcessing.com for more great signal-processing content: ad-free videos, concept/screenshot files, quizzes, MATLAB and data files. Includes definitions of binary and m-ary tests, simple and composite hypotheses, decision regions, and test performance characterization: prob
From playlist Estimation and Detection Theory