Presentation is loading. Please wait.

Presentation is loading. Please wait.

PROBABILITY. CONDITIONAL PROBABILITY Random variable A variable defined on a sample space. Fx: The value of a card. Interpretation: A variable that takes.

Published by Modified over 9 years ago

Similar presentations

Presentation on theme: "PROBABILITY. CONDITIONAL PROBABILITY Random variable A variable defined on a sample space. Fx: The value of a card. Interpretation: A variable that takes."— Presentation transcript:

1 PROBABILITY

2 CONDITIONAL PROBABILITY

3 Random variable A variable defined on a sample space. Fx: The value of a card. Interpretation: A variable that takes different values with different probabilities. (Some) Characteristics of a random variable X: Mean value E(X). Variation V(X) = E((X-E(x))^2). Graphical representation by histogram. Cumulative mass function/distribution function of a random variable: F(x) = P(X ≤ x)

4 BINOMIAL DISTRIBUTION

5

6

7 POISSON DISTRIBUTION

8

9

10

11 CONTINOUS DISTRIBUTIONS

12

13 NORMAL DISTRIBUTION

14

15

16

17 LOG-NORMAL DISTRIBUTION

18 Fractile/QQ-plots How can we access information about the distribution of a sample? By comparing fractiles – the QQ-plot in SPSS. The proposed distribution is good, if the fractiles follow a linear pattern. Notice: The variability of the points decreases when the sample size increases. The variation of the points around the line is largest in the ends. Hence, pay more attention to the points in the middle of the plot. Detrended QQ-plots The points should be spread evenly above/below the horizontal line. There should be no pattern.

19 Examples of QQ-plots Normal distributionSkew distribution Uniform distribution QQ-plot Detrended QQ-plot

Download ppt "PROBABILITY. CONDITIONAL PROBABILITY Random variable A variable defined on a sample space. Fx: The value of a card. Interpretation: A variable that takes."

Similar presentations

Special random variables Chapter 5 Some discrete or continuous probability distributions.

Special random variables Chapter 5 Some discrete or continuous probability distributions.
Probability Distribution

Probability Distribution
Graphics Calculator Probability Distributions Graphics Calculator Binomial Dist Graphics Calc Poisson Dist Graphics Calc Normal Dist.

Graphics Calculator Probability Distributions Graphics Calculator Binomial Dist Graphics Calc Poisson Dist Graphics Calc Normal Dist.
Continuous Probability Distributions.  Experiments can lead to continuous responses i.e. values that do not have to be whole numbers. For example: height.

Continuous Probability Distributions.  Experiments can lead to continuous responses i.e. values that do not have to be whole numbers. For example: height.
Probability Distribution

Probability Distribution
Review of Basic Probability and Statistics

Review of Basic Probability and Statistics
Engineering Probability and Statistics - SE-205 -Chap 4 By S. O. Duffuaa.

Engineering Probability and Statistics - SE-205 -Chap 4 By S. O. Duffuaa.
Probability Densities

Probability Densities
1 Engineering Computation Part 6. 2 Probability density function.

1 Engineering Computation Part 6. 2 Probability density function.
Probability Distributions

Probability Distributions
Stat 470-11 Today: More Chapter 3. Assessing Effect Significance For replicated experiments, can use regression to determine important effects Can also.

Stat Today: More Chapter 3. Assessing Effect Significance For replicated experiments, can use regression to determine important effects Can also.
Samples vs. Distributions Distributions: Discrete Random Variable Distributions: Continuous Random Variable Another Situation: Sample of Data.

Samples vs. Distributions Distributions: Discrete Random Variable Distributions: Continuous Random Variable Another Situation: Sample of Data.
Probability and Statistics Review

Probability and Statistics Review
2. Random variables  Introduction  Distribution of a random variable  Distribution function properties  Discrete random variables  Point mass  Discrete.

2. Random variables  Introduction  Distribution of a random variable  Distribution function properties  Discrete random variables  Point mass  Discrete.
Copyright (c) 2004 Brooks/Cole, a division of Thomson Learning, Inc. Chapter 4 Continuous Random Variables and Probability Distributions.

Copyright (c) 2004 Brooks/Cole, a division of Thomson Learning, Inc. Chapter 4 Continuous Random Variables and Probability Distributions.
Chapter 21 Random Variables Discrete: Bernoulli, Binomial, Geometric, Poisson Continuous: Uniform, Exponential, Gamma, Normal Expectation & Variance, Joint.

Chapter 21 Random Variables Discrete: Bernoulli, Binomial, Geometric, Poisson Continuous: Uniform, Exponential, Gamma, Normal Expectation & Variance, Joint.
4-1 Continuous Random Variables 4-2 Probability Distributions and Probability Density Functions Figure 4-1 Density function of a loading on a long,

4-1 Continuous Random Variables 4-2 Probability Distributions and Probability Density Functions Figure 4-1 Density function of a loading on a long,
Discrete Probability Distributions A sample space can be difficult to describe and work with if its elements are not numeric.A sample space can be difficult.

Discrete Probability Distributions A sample space can be difficult to describe and work with if its elements are not numeric.A sample space can be difficult.
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Review of Exam 2 Sections 4.6 – 5.6 Jiaping Wang Department of Mathematical Science 04/01/2013, Monday.

The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Review of Exam 2 Sections 4.6 – 5.6 Jiaping Wang Department of Mathematical Science 04/01/2013, Monday.
McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.

Similar presentations

Ads by Google