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Standard Normal DistributionSymmetric about peak at mean Mean = µ and Standard deviation = σ Standard Normal with µ = 0 and σ = 1 Symmetric about peak at 0 Stretches from about -3 to 3
Standardization: Converting a Normal into the Standard NormalIf X is a normal random variable with Mean = µ and Standard deviation = σ let What is the distribution of S? Explain
Standardization and the Central Limit TheoremCLT says that has mean and standard deviation and standard deviation Thus the standardized sample mean has the standard normal distribution
The Normal Distribution
How many movies do you watch? Does the CLT apply to means? The Central Limit Theorem states that the more samples you take, the more Normal your.
Section 5.3 ~ The Central Limit Theorem Introduction to Probability and Statistics Ms. Young ~ room 113.
For a Normal probability distribution, let x be a random variable with a normal distribution whose mean is µ and whose standard deviation is σ. Let be.
Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide
Use of moment generating functions. Definition Let X denote a random variable with probability density function f(x) if continuous (probability mass function.
Sampling distributions. Example Take random sample of students. Ask “how many courses did you study for this past weekend?” Calculate a statistic, say,
5.2 The Sampling Distribution of a Sample Mean
Distribution of Sample Means, the Central Limit Theorem If we take a new sample, the sample mean varies. Thus the sample mean has a distribution, called.
DISTRIBUTION OF THE SAMPLE MEAN
1 Trust and divorce Separated or Divorced trust | No Yes | Total Low | | 247 | |
Chapter Six Sampling Distributions McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter 8 – Normal Probability Distribution A probability distribution in which the random variable is continuous is a continuous probability distribution.
4. Convergence of random variables Convergence in probability Convergence in distribution Convergence in quadratic mean Properties The law of.
Lesson #17 Sampling Distributions. The mean of a sampling distribution is called the expected value of the statistic. The standard deviation of a sampling.
Chapter 7: Variation in repeated samples – Sampling distributions
2003/04/24 Chapter 5 1頁1頁 Chapter 5 : Sums of Random Variables & Long-Term Averages 5.1 Sums of Random Variables.
Chapter 11: Random Sampling and Sampling Distributions
Clt1 CENTRAL LIMIT THEOREM specifies a theoretical distribution formulated by the selection of all possible random samples of a fixed size n a sample.
Sample Distribution Models for Means and Proportions
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