'Random variable x' presentation slideshows

Chapter 6 Probability Distributions

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Chapter 2:

Chapter 2:. Probability. Section 2.1: Basic Ideas. Definition: An experiment is a process that results in an outcome that cannot be predicted in advance with certainty. Examples: rolling a die tossing a coin weighing the contents of a box of cereal. Sample Space.

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Uncertainty

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Moment Generating Functions

Moment Generating Functions. The Uniform distribution from a to b. Continuous Distributions. The Normal distribution (mean m , standard deviation s ). The Exponential distribution. Weibull distribution with parameters a and b . The Weibull density, f ( x ). ( a = 0.9, b = 2).

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Confidence Intervals

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Random Variables

Random Variables. Discrete Random Variables. For a discrete random variable X the probability distribution is described by the probability function p ( x ) = P [ X = x ], which has the following properties:. Continuous random variables.

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Appendix B

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Nuts and Bolts cont.

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CHAPTER 4 EXPECTATION

CHAPTER 4 EXPECTATION. CHAPTER 4. Overview. ? The Expectation of a R. V. ? Properties of Expectation ? Variance ? Moments ? The Mean and the Median ? Covariance and Correlation ? Conditional Expectation ? The Sample Mean. Section 4.1 The Expectation of a Random Variable.

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CHAPTER 5 REVIEW

CHAPTER 5 REVIEW.

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4.2 (cont.) Expected Value of a Discrete Random Variable

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P robability Models & Applications

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Probability Theory and Measure

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Why Probability?

Why Probability? Probability theory describes the likelihood of observing various outcomes for a given population Statistics uses rules of probability as a tool for making inferences about or describing a population using data from a sample Some Concepts

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All of Statistics Chapter 5: Convergence of Random Variables

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Probability & Statistics for Engineers & Scientists, by Walpole, Myers, Myers & Ye ~ Chapter 8 Notes

Probability & Statistics for Engineers & Scientists, by Walpole, Myers, Myers & Ye ~ Chapter 8 Notes. Class notes for ISE 201 San Jose State University Industrial & Systems Engineering Dept. Steve Kennedy. Populations & Samples.

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Chapter 6 The Normal Distribution

Chapter 6 The Normal Distribution. In this handout: Probability model for a continuous random variable Normal distribution. The idea of a continuous probability distribution draws from the relative frequency histogram for a large number of measurements (recall chapter 2).

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Theorems about mean, variance

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Random Variables

Random Variables. A random variable is a rule that assigns exactly one value to each point in a sample space for an experiment. A random variable can be classified as being either discrete or continuous depending on the numerical values it assumes.

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Characteristic Functions

Characteristic Functions. 1. Bernoulli Distribution . he Bernoulli distribution is a discrete distribution having two possible outcomes labelled by n=0 and n=1 in which n=1 ("success") occurs with probability p

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