Combining Independent Random Variables, Statistics

Statistics > Combining Independent Random Variables

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Combining Independent Random Variables

If two random variables are independent, their joint probability is the product of the two marginal probabilities.
The mean of the sum of independent random variables is the sum of the means of the independent random variables.
The variance of the sum of independent random variables is the sum of the variances of the independent random variables.

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Table of Contents

I. Introduction
	Basic Ideas	17:34
II. Exploring Data
	Raw Data, Dotplots, Stemplots	27:24
	Histograms, Cumulative Frequency Plots	10:21
	Summarizing Distributions, Measuring Center	16:43
	Measuring Spread: Range, IQR, Standard Deviation	18:04
	Measuring Position: Quartiles, Percentiles, Standardized Scores	16:28
	Boxplots	10:07
	Comparing Distributions of Univariate Data	24:19
	Exploring Bivariate Data: Scatterplots	13:45
	Least Squares Regression	17:32
	Exploring Categorical Data	17:00
III. Sampling and Experimentation
	Methods of Data Collection	12:04
	Planning and Conducting Surveys	13:51
	Planning and Conducting Experiments	19:32
IV. Probability
	Experiment, Outcomes, and Sample Space	14:54
	Calculating Probability	14:13
	Probability and Events	22:08
	Intersection of Events and the Multiplication Rule	19:58
	Union of Events and the Addition Rule	18:28
	Bayes' Rule	16:59
V. Discrete Random Variables and Probability Distribution
	Random Variables	7:52
	Probability Distribution of a Discrete Random Variable	15:55
	Mean and Standard Deviation of a Discrete Random Variable	17:37
	Factorials, Combinations, Permutations	15:43
	Binomial Probability Distribution	21:38
	Poisson Probability Distribution	13:40
	Geometric and Hypergeometric Probability Distributions	19:08
	Combining Independent Random Variables	20:26
VI. Continuous Random Variables and the Normal Distribution
	Continuous Probability Distribution	6:19
	Normal Distribution	6:42
	Standard Normal Distribution	13:25
	Standardizing a Normal Distribution	12:22
	Applications of the Normal Distribution	12:20
	Finding Values When the Probability is Known	12:44
VII. Sampling Distributions
	Population and Sampling Distributions	12:02
	Mean, Standard Deviation, and the Shape of the Sampling Distribution of the Sampling Mean	4:57
	Applications of the Sampling Distribution of the Sample Mean	14:50
	Mean, Standard Deviation, and the Shape of the Sampling Distribution of the Sample Proportion	3:58
	Applications of the Sampling Distribution of the Sample Proportion	10:45
VIII. Estimation of the Mean and Proportion
	Introduction to Estimation	12:52
	Estimation of a Population Mean: Standard Deviation Known	17:03
	Sample Size for Estimation of a Population Mean	10:39
	Estimation of Population Mean: Sigma Not Known	19:25
	Estimation of Population Proportion: Large Sample	17:26
	Large Sample Confidence Intervals for Difference in Population Proportion	16:16
	Confidence Intervals for a Difference in Means	27:58
	Confidence Intervals for the Slope of a Least Squares Regression Line	18:47
IX. Tests of Significance
	Introduction: Hypothesis Tests	14:09
	Large Sample Test for a Proportion	14:30
	Large Sample Test for a Difference in Two Proportions	19:14
	Test for a Mean	14:57
	Test for a Difference Between Two Means	23:13
	Chi-Square Tests: One Way and Two Way	24:33
	Hypothesis Testing for the Slope of a Least Squares Regression Line	17:48