Mean and Standard Deviation of a Discrete Random Variable, Statistics

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Mean and Standard Deviation of a Discrete Random Variable

The mean of a discrete random variable is .
The standard deviation of a discrete random variable is
When using the “easier” equation for the standard deviation, do not forget to subtract from .

Mean and Standard Deviation of a Discrete Random Variable

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

Intro

Mean of a Discrete Random Variable

Example

Example: Numbers Game

Standard Deviation of a Discrete Random Variable

Example

Example: Cars in a Town

Extra Example 1

Extra Example 2

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	16:04
	Measuring Spread: Range, IQR, Standard Deviation	18:04
	Measuring Position: Quartiles, Percentiles, Standardized Scores	16:28
	Boxplots	15:37
	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

Mathematics: AP Statistics

I. Introduction
	Basic Ideas			17:34
		Intro		0:00
		Basic Definitions		0:09
			Element (member, unit)	0:20
			Variable	1:01
			Observation (measurement)	1:18
			Data Set	1:40
		Example: Basic Definitions		1:55
		Qualitative Variables		4:58
		Quantitative Variables		6:16
			Discrete Variable	6:33
			Continuous Variable	7:36
		Cross Section vs Time Series Data		8:58
		Summation Notation		10:50
		Summation Notation 2		12:59
		Summation Notation 3		15:32
II. Exploring Data
	Raw Data, Dotplots, Stemplots			27:24
		Intro		0:00
		Raw Data		0:07
			Ungrouped Data	0:25
			Example: Ages	0:39
		Features of Graphical Displays of Distributions		1:28
			Center and Spread	1:54
			Clusters and Gaps	2:04
			Outliers (extreme values)	2:12
			Symmetric	2:48
			Skewed	3:14
			Uniform	3:47
		Dotplots		4:58
		Example: Dotplots		8:51
		Stemplot		11:12
			Stem and Leaf	11:17
		Example: Stemplot		15:18
		Extra Example 1		3:48
		Extra Example 2		4:00
	Histograms, Cumulative Frequency Plots			10:21
		Intro		0:00
		Features of Graphical Displays of Distributions		0:07
		Histogram		3:03
			Common Programs	3:09
		Example: Histogram		6:14
		Cumulative Frequency Plot		7:43
		Example: Cumulative Frequency Plot		8:16
	Summarizing Distributions, Measuring Center			16:04
		Intro		0:00
		Measures of Central Tendency		0:08
		Mean (average)		0:28
			Mean for Population Data	0:51
			Mean for Sample Data	1:18
		Example: Mean		1:57
		Example: Mean		2:49
		Median		3:53
		Example: Median		4:52
		Example: Median		6:47
		Mode		8:01
			Unimodal	8:11
			Bimodal	8:19
			Multimodal	8:24
		Example: Mode		8:34
		Example: Mode		9:53
		Effect of Changing Units		10:31
		Extra Example 1		1:53
		Extra Example 2		1:36
	Measuring Spread: Range, IQR, Standard Deviation			18:04
		Intro		0:00
		Measuring Spread		0:08
		Range		1:06
			Example	1:16
			Example	1:35
		Standard Deviation		2:05
			Population Standard Deviation	2:14
			Sample Standard Deviation	3:13
		Example: Standard Deviation		4:11
		Example: Standard Deviation		6:05
		Interquartile Range (IQR)		8:05
		Example: Interquartile Range		9:03
		Example: Interquartile Range		10:27
		Extra Example 1		3:15
		Extra Example 2		2:28
	Measuring Position: Quartiles, Percentiles, Standardized Scores			16:28
		Intro		0:00
		Measure of Position		0:09
			Quartile, Percentile, Z-Scores	0:24
		Quartiles (Q1, Q2, Q3)		0:32
			Example	0:51
		Example: Quartiles		1:28
		Example: Quartiles		3:27
		Percentiles		5:44
		Example: Percentiles		6:19
		Example: Percentiles		7:24
		Standardized Score (Z-Score)		8:27
		Example: Standardized Score		9:23
		Example: Standardized Score		10:21
		Extra Example 1		2:56
		Extra Example 2		2:11
	Boxplots			15:37
		Intro		0:00
		What is a Boxplot?		0:05
			Five Number Summary	0:15
		Example: Boxplot		0:30
		Example: Boxplot		4:33
		Extra Example 1		3:09
		Extra Example 2		2:21
	Comparing Distributions of Univariate Data			24:19
		Intro		0:00
		Comparing Features		0:07
			Compare Center & Spread	0:11
			Compare Clusters & Gaps	0:23
			Compare Outliers and Unusual Features	0:33
			Compare Shapes	0:55
			Symmetric	1:00
			Skewed Right	1:20
			Skewed Left	1:31
			Uniform	1:41
		Example: Dotplots		1:56
		Example: Back to Back Stemplots		5:16
		Example: Parallel Boxplots		10:21
		Example: Back to Back Stemplots		15:03
		Extra Example 1		2:00
		Extra Example 2		5:06
	Exploring Bivariate Data: Scatterplots			13:45
		Intro		0:00
		Bivariate Data		0:08
			Example: Student Scores	0:31
		Example: Scatterplot		1:08
		Example: Scatterplot		2:36
		Correlation and Linearity		3:49
		Example: Correlation		5:30
		Example: Correlation		6:55
		Extra Example 1		3:10
		Extra Example 2		2:21
	Least Squares Regression			17:32
		Intro		0:00
		Least Squares Regression Line		0:06
			Why Least Squares?	0:25
			Equations	1:21
		Example 1: Age and Price		2:02
		Example 2: Weld Diameter		5:47
		Diagnostics		8:39
			Residuals	8:58
			Normal Probability Plot	10:09
			Studentized Residuals (Hat Matrix)	10:29
		Transformations		10:48
			Logarithmic Transformation	11:04
			Square Root Transformation	11:44
		Extra Example 1		3:07
		Extra Example 2		2:11
	Exploring Categorical Data			17:00
		Intro		0:00
		Frequency Tables		0:05
			Example: Student Age	0:16
			Relative Frequency	0:55
		Bar Graphs		1:59
		Marginal and Joint Probabilities		3:54
		Example 1: Gender and Beer		6:52
		Conditional Probabilities		8:47
		Example 2: Gender and Beer		11:41
		Extra Example 1		2:09
		Extra Example 2		1:56
III. Sampling and Experimentation
	Methods of Data Collection			12:04
		Intro		0:00
		Purpose		0:05
		Census		1:22
			Example: US Census	1:36
			Example: Fireworks Factory	2:34
		Sample Survey		3:41
		Experiment		6:12
			Example: Coke vs Pepsi	7:09
		Observational Study		8:19
		Observational or Experiment		9:30
			Example 1	9:53
			Example 2	10:24
			Example 3	11:17
	Planning and Conducting Surveys			13:51
		Intro		0:00
		Ideal Surveys		0:06
			Random Selection	0:16
		Characteristics of Surveys		0:42
			Chance	0:50
			Random Samples	1:02
			No Source of Bias	1:32
		Populations, Samples, Random Selection		2:21
			Population	2:28
			Sample	2:51
		Sources of Bias		4:14
			Example	4:33
		Sampling Methods		7:27
			Simple Random Sampling (SRS)	7:40
			Example	8:33
			Stratified Random Sampling (Strata)	10:03
			Example	11:06
			Cluster Sampling	12:19
			Example	13:06
	Planning and Conducting Experiments			19:32
		Intro		0:00
		Purpose		0:06
		Characteristics		1:00
		Basic Terms		2:00
			Treatment	2:12
			Control Group	2:30
			Experimental Units	3:17
			Random Assignment	3:38
			Replication	4:19
		Sources of Bias and Confounding		4:48
			Counfounding	5:00
			Example	5:29
			Placebo Effect	6:41
			Example	7:08
			Blinding	7:56
			Example	8:24
		Completely Randomized Design		9:12
		Randomized Block Design		12:44
			Block	12:55
			Matched Pairs	13:22
			Example	13:41
			Randomized Block Design	15:09
			Example	15:30
		Studies and Surveys vs Experiments		17:03
IV. Probability
	Experiment, Outcomes, and Sample Space			14:54
		Intro		0:00
		Basic Definitions		0:29
			Experiment	0:35
			Outcomes	0:55
			Sample Space	1:04
		Examples		1:34
			Roll a Die	1:39
			Flip a Coin	2:33
		Simple and Compound Events		3:30
			Event	3:43
			Simple Event	3:58
			Compound Event	4:27
		Example		5:14
		Extra Example 1		0:59
		Extra Example 2		4:21
	Calculating Probability			14:13
		Intro		0:00
		What is Probability		0:27
			Range	0:53
			Sum of Probabilities	1:26
			Example: Football Game	2:05
		Classical Probability		2:53
			Equally Likely Outcomes	3:05
			Example: Coin Flip	4:08
			Example: Die Roll	5:12
		Relative Frequency		6:44
			Example	7:22
		Subjective Probability		9:38
			Example	10:06
		Extra Example 1		1:04
		Extra Example 2		1:33
	Probability and Events			22:08
		Intro		0:00
		Mutually Exclusive Events		0:17
			Example: Coin Flip	0:27
			Example: Die Roll	3:03
		Independent Events		5:13
			Notation	3:31
			Example: Coin	6:01
		Independent Events, cont.		9:19
			Example: Coffee Drinkers	9:23
		Mutually Exclusive vs Independent		13:03
		Complementary Events		14:08
			Example: Coffee Drinkers	15:37
		Extra Example 1		1:16
		Extra Example 2		3:32
	Intersection of Events and the Multiplication Rule			19:58
		Intro		0:00
		Intersection of Events		0:08
			Venn Diagram	1:20
		Multiplication Rule		2:22
			Joint Probability	2:23
			Example	3:23
		Example		6:30
		Multiplication Rule for Independent Events		10:30
			Example	11:39
		Joint Probability of Mutually Exclusive Events		15:24
		Extra Example 1		1:24
		Extra Example 2		2:09
	Union of Events and the Addition Rule			18:28
		Intro		0:00
		Union of Events		0:06
			Venn Diagram	0:52
		Addition Rule		2:01
			Example: Coffee Drinkers	3:25
		Example		6:26
		Addition Rule for Mutually Exclusive Events		9:11
		Example		10:27
		Extra Example 1		2:41
		Extra Example 2		1:15
	Bayes' Rule			16:59
		Intro		0:00
		Partition of Events		0:07
			Venn Diagram	0:17
		Law of Total Probability		3:12
		Bayes' Rule		6:11
		Example		9:09
		Extra Example 1		4:07
V. Discrete Random Variables and Probability Distribution
	Random Variables			7:52
		Intro		0:00
		Definition		0:06
			Example	0:24
		Discrete Random Variables		1:22
			Example	1:56
		Continuous Random Variable		3:53
			Example	4:12
		Extra Example 1		1:51
	Probability Distribution of a Discrete Random Variable			15:55
		Intro		0:00
		Definition		0:09
			Example	0:24
		Rules of a Probability Distribution		3:27
			Rule 1	3:33
			Rule 2	4:30
			Example 1	4:59
			Example 2	6:00
			Example 3	6:38
		Example: Defective DVDs		7:19
		Extra Example 1		1:56
		Extra Example 2		1:28
	Mean and Standard Deviation of a Discrete Random Variable			17:37
		Intro		0:00
		Mean of a Discrete Random Variable		0:10
			Example	1:17
		Example: Numbers Game		3:09
		Standard Deviation of a Discrete Random Variable		6:02
			Example	7:46
		Example: Cars in a Town		10:12
		Extra Example 1		2:24
		Extra Example 2		2:22
	Factorials, Combinations, Permutations			15:43
		Intro		0:00
		Counting Rule		0:08
			Example: Coin Toss	0:56
			Example: Football Team	1:45
		Factorials		2:54
			Example	3:39
			Zero Factorial	4:03
			Example	4:20
		Combinations		5:16
			Example	6:23
		Permutations		8:16
			Example	9:01
		Extra Example 1		2:58
		Extra Example 2		2:20
	Binomial Probability Distribution			21:38
		Intro		0:00
		Binomial Experiment		0:07
			Discrete Random Variable	0:34
			Trial	1:01
			Bernoulli Trials	1:26
		Example: Roll Die		2:37
		Binomial Probability Distribution		4:36
		Example: Winter Holiday Stress		6:58
		Example: MRI		9:51
		Probability of Success and Shape		12:42
			Symmetric	12:54
			Skewed Right	13:23
			Skewed Left	14:13
		Mean/Standard Deviation of Binomial Distribution		15:03
			Example: Stress	16:06
			Example: MRI	17:07
		Extra Example 1		1:47
		Extra Example 2		1:49
	Poisson Probability Distribution			13:40
		Intro		0:00
		Poisson Probability Distribution		0:06
			Conditions	0:43
		Example: Complaints		3:18
		Example: Failed Businesses		5:01
		Mean/Standard Deviation of Poisson Distribution		7:52
			Example: Complaints	8:53
			Example: Failed Businesses	9:46
		Extra Example 1		1:19
		Extra Example 2		1:48
	Geometric and Hypergeometric Probability Distributions			19:08
		Intro		0:00
		Geometric Probability Distribution		0:08
		Example: Engine Malfunction		3:00
		Example: Interviews		5:45
		Hypergeometric Probability Distribution		7:36
		Example: Engineers		10:16
		Example: Marbles		12:55
		Extra Example 1		1:14
		Extra Example 2		2:00
	Combining Independent Random Variables			20:26
		Intro		0:00
		Independence vs Dependence		0:09
		Mean of Sums for Independent Random Variables		2:32
		Example		4:02
		Example		5:58
		Variance for Sums of Independent Random Variables		8:49
		Example		10:30
		Example		12:26
		Extra Example 1		3:04
		Extra Example 2		1:59
VI. Continuous Random Variables and the Normal Distribution
	Continuous Probability Distribution			6:19
		Intro		0:00
		Continuous Random Variable		0:07
		Probability Density Function		0:54
		More About Densities		3:07
		More About Densities, cont.		4:06
	Normal Distribution			6:42
		Intro		0:00
		Normal Distribution		0:05
			Bell Shaped Curve	0:09
		Properties of the Normal Distribution		1:02
			Area Under the Curve (Density Curve)	1:07
		Symmetric About the Mean		1:40
		Two Tails		2:21
		Normal Distribution		3:07
			Different Means	3:10
		Different Standard Deviations		4:32
	Standard Normal Distribution			13:25
		Intro		0:00
		Standard Normal Distribution		0:06
			Z-Scores	1:08
		Examples		1:57
		More Examples		4:43
		More Examples		7:12
		Extra Example 1		1:51
		Extra Example 2		1:33
	Standardizing a Normal Distribution			12:22
		Intro		0:00
		Standardizing a Normal Distribution		0:07
			Mean and Standard Deviation of X	1:13
		Examples		1:39
		More Examples		3:22
		More Examples		6:17
		Extra Example 1		1:55
		Extra Example 2		1:12
	Applications of the Normal Distribution			12:20
		Intro		0:00
		Standardizing a Normal Distribution		0:08
		Example: US Debt		0:59
		Example: Toy Assembly		3:19
		Example: Soda		5:04
		Example: Calculator		7:27
		Extra Example 1		1:31
		Extra Example 2		1:45
	Finding Values When the Probability is Known			12:44
		Intro		0:00
		Example 1		0:10
		Example 2		1:32
		Example 3		3:12
		Example 4: Battery Life		4:18
		Example 5: SAT Scores		6:33
		Extra Example 1		1:24
		Extra Example 2		2:21
VII. Sampling Distributions
	Population and Sampling Distributions			12:02
		Intro		0:00
		Population Distribution		0:06
			Example: Teaching Experience	0:14
		Sampling Distribution		1:31
		Example: Teaching Experience		2:16
		Sampling Error		5:29
			Random and No Non-Sampling Error	6:00
			Example	6:10
		Non-Sampling Error		7:22
			Example	7:38
		Example: Six Numbers		9:17
	Mean, Standard Deviation, and the Shape of the Sampling Distribution of the Sampling Mean			4:57
		Intro		0:00
		Mean/Standard Deviation of Sample Mean		0:10
			Estimator	0:57
			Unbiased Estimator	1:15
		Sampling Distribution of Sample Mean		1:50
			Spread	1:53
			Standard Deviation	2:18
			Consistent Estimator	2:40
		Shape of Sampling Distribution		2:51
			Normal	3:21
		Shape of Sampling Distribution, cont.		3:50
			Central Limit Theorem	4:15
	Applications of the Sampling Distribution of the Sample Mean			14:50
		Intro		0:00
		Example 1: Speed Limit		0:08
		Example 2: Speed Limit		2:50
		Example 3: Speed Limit		4:20
		Example 4: Study Times		6:20
		Example 5: Study Times		9:02
		Extra Example 1		2:14
		Extra Example 2		2:12
	Mean, Standard Deviation, and the Shape of the Sampling Distribution of the Sample Proportion			3:58
		Intro		0:00
		Population vs Sample Proportions		0:10
			Population Proportion	0:16
			Sample Proportion	0:23
			Sample: Eye Color	0:36
		Mean/Standard Deviation of Sample Proportion		1:47
			Mean	1:51
			Unbiased Estimator	2:07
			Standard Deviation	2:28
		Shape of the Distribution		3:07
	Applications of the Sampling Distribution of the Sample Proportion			10:45
		Intro		0:00
		Example 1: Retirement Plan		0:07
		Example 2: Retirement Plan		3:04
		Example 3: Voters		4:35
		Extra Example 1		2:27
		Extra Example 2		1:40
VIII. Estimation of the Mean and Proportion
	Introduction to Estimation			12:52
		Intro		0:00
		Estimation		0:06
			Parameter	0:29
			Estimate	1:02
			Estimator	1:10
			Example	1:20
		Steps for Estimation		2:21
			Example: Dartboard	3:08
			Consistent/Bias	3:41
			Inconsistent/Unbiased	4:09
			Consistent/Unbiased	4:44
		Point Estimate		5:33
			Example	5:50
		Interval Estimate		6:35
			Margin of Error	7:15
		Confidence Interval		7:35
			Confidence Level	7:55
		Example		8:10
		More on Confidence Intervals		10:18
			Confidence Level Increase	11:41
			Sample Size Increase	12:25
	Estimation of a Population Mean: Standard Deviation Known			17:03
		Intro		0:00
		Population is Normal, n<30		0:10
			Confidence Interval	0:28
		Example 1		2:34
		Example 2		5:54
		When n>30, Any Distribution		7:58
			Confidence Interval	8:48
		Example 3		9:14
		Example 4		11:16
		Extra Example 1		2:24
		Extra Example 2		1:34
	Sample Size for Estimation of a Population Mean			10:39
		Intro		0:00
		Determining Sample Size		0:07
			Finding n	0:30
			Origin of Equation	0:56
		Example 1		2:16
		Example 2		4:42
		Extra Example 1		2:13
		Extra Example 2		1:43
	Estimation of Population Mean: Sigma Not Known			19:25
		Intro		0:00
		t-Distribution		0:10
		Examples: t-Distribution		0:38
		Using the t-Distribution		4:25
			Confidence Interval	5:03
		Example 1: Waiting Time		5:54
		Example 2: MPG		9:35
		Extra Example 1		3:23
		Extra Example 2		2:54
	Estimation of Population Proportion: Large Sample			17:26
		Intro		0:00
		Population vs Sample Proportion		0:10
		Confidence Intervals for p		1:50
		Example 1: Credit		2:18
		Example 2: Time		4:59
		Sample Size for the Estimation of p		7:31
			Margin of Error	7:55
			Conservative Estimate	8:17
		Example 3: Gambling		8:40
		Example 4: Clocks		10:53
		Extra Example 1		2:32
		Extra Example 2		1:50
	Large Sample Confidence Intervals for Difference in Population Proportion			16:16
		Intro		0:00
		Sampling Distribution for Difference in Sample Proportion		0:08
			Large and Independent Samples	0:11
			Confidence Intervals for p1-p2	1:28
		Example 1: Toothpaste		2:04
		Example 2: Seat Belts		6:20
		Extra Example 1		3:32
		Extra Example 2		2:50
	Confidence Intervals for a Difference in Means			27:58
		Intro		0:00
		Independent Samples: Standard Deviations Known		0:07
		Confidence Interval for Difference of Means		1:12
		Example 1: Starting Salary		1:35
		Example 2: Fill		5:36
		Independent Samples: Standard Deviations Not Known		7:54
		Pooled Standard Deviation for Two Samples		8:46
		Confidence Interval for Difference of Means		9:32
		Example 3: Caffeine		10:35
		Example 4: Test Scores		15:20
		Inference about Difference of Means for Paired Samples		19:05
			Paired or Matched Sample	19:21
		Inference about Difference of Means for Paired Samples		20:58
		Extra Example 1		3:40
		Extra Example 2		2:03
	Confidence Intervals for the Slope of a Least Squares Regression Line			18:47
		Intro		0:00
		Sampling Distribution of b		0:08
		Calculating the Estimator of Standard Deviation of b		1:03
		Confidence Interval for Beta		1:31
		Example 1: Age and Price		2:24
		Example 2: Weld Diameter		6:41
		Extra Example 1		4:27
		Extra Example 2		3:37
IX. Tests of Significance
	Introduction: Hypothesis Tests			14:09
		Intro		0:00
		Two Hypotheses		0:13
			Null Hypothesis	0:21
			Alternative Hypothesis	0:36
			Example	1:05
		Example: Two Hypotheses		1:43
		Rejection and Non-Rejection Regions		3:25
		Type 1 and Type 2 Errors		5:30
			Type 1 Error	6:44
			Significance Level	7:08
			Type 2 Error	7:42
			Power of the Test	8:30
		Tails of the Test		9:29
	Large Sample Test for a Proportion			14:30
		Intro		0:00
		Test Statistic Z		0:08
			Why Z?	0:29
		Example 1: TV Violence		1:10
		Example 2: Smoking		5:16
		Extra Example 1		3:25
		Extra Example 2		2:52
	Large Sample Test for a Difference in Two Proportions			19:14
		Intro		0:00
		Pooled Estimate of P1 and P2		0:09
		Example 1: Softball Bases		1:34
		Example 2: Sleep Problems		6:59
		Extra Example 1		4:11
		Extra Example 2		4:12
	Test for a Mean			14:57
		Intro		0:00
		Standard Deviation is Known		0:07
			Central Limit Theory for n>30	0:32
		Example 1: Cheese Weight		0:53
		Example 2: Observations		3:53
		Standard Deviation Not Known		6:15
			t-Distribution Usage	6:24
			Degrees of Freedom	6:53
		Example 3: Height		7:01
		Example 4: Sampling		9:50
		Extra Example 1		2:02
		Extra Example 2		1:32
	Test for a Difference Between Two Means			23:13
		Intro		0:00
		Standard Deviation Known, Unpaired		0:08
		Example 1: Boredom		1:17
		Example 2: Smoking		4:15
		Population Standard Deviations Unknown, But Equal		7:10
			Pooled Standard Deviation for Two Samples	7:49
		Example 3: Diet Soda		8:28
		Example 4: TV		12:12
		Paired Samples		15:50
		Example 5: Hormone Level		16:33
		Example 6: Hypnotism		19:43
	Chi-Square Tests: One Way and Two Way			24:33
		Intro		0:00
		Goodness of Fit Test		0:07
			Right-Tailed Test	0:52
		Example 1: Die Rolls		1:16
		Example 2: Stolen Vehicles		3:31
		Test of Independence		7:02
		Example 3: Debt		7:51
		Example 4: Contraceptive Use		13:14
		Test of Homogeneity		16:31
		Example 5: New Product		17:09
		Example 6: Oil		21:24
	Hypothesis Testing for the Slope of a Least Squares Regression Line			17:48
		Intro		0:00
		Sampling Distribution of b		0:08
		Calculating the Estimator of Standard Deviation of b		1:18
		Hypothesis Testing for Beta		1:50
		Example 1: Age		2:25
		Example 2: Weld Diameter		6:42
		Extra Example 1		3:30
		Extra Example 2		3:10

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Mean and Standard Deviation of a Discrete Random Variable

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Mean and Standard Deviation of a Discrete Random Variable

Mean and Standard Deviation of a Discrete Random Variable

Mathematics: AP Statistics

Related Books

Related Books

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