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Engineering Statistics - IE 261 Chapter 4 Continuous Random Variables and Probability Distributions...

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Engineering Statistics - IE 261 Chapter 4 Continuous Random Variables and Probability Distributions URL: http://home.npru.ac.th/piya/Classe sTU.html http://home.npru.ac.th/piya/ webscilab
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Page 1: Engineering Statistics - IE 261 Chapter 4 Continuous Random Variables and Probability Distributions URL:  tml .

Engineering Statistics - IE 261

Chapter 4Continuous Random Variables andProbability Distributions

URL: http://home.npru.ac.th/piya/ClassesTU.html

http://home.npru.ac.th/piya/webscilab

Page 2: Engineering Statistics - IE 261 Chapter 4 Continuous Random Variables and Probability Distributions URL:  tml .

4-1 Continuous Random Variables

current in a copper wirelength of a machined part

Continuous random variable X

Page 3: Engineering Statistics - IE 261 Chapter 4 Continuous Random Variables and Probability Distributions URL:  tml .

4-2 Probability Distributions and Probability Density Functions

Figure 4-1 Density function of a loading on a long, thin beam.

• For any point x along the beam, the density can be described by a function (in grams/cm)• The total loading between points a and b is determined as the integral of the density function

from a to b.

Page 4: Engineering Statistics - IE 261 Chapter 4 Continuous Random Variables and Probability Distributions URL:  tml .

4-2 Probability Distributions and Probability Density Functions

Figure 4-2 Probability determined from the area under f(x).

Page 5: Engineering Statistics - IE 261 Chapter 4 Continuous Random Variables and Probability Distributions URL:  tml .

4-2 Probability Distributions and Probability Density Functions

Definition

Page 6: Engineering Statistics - IE 261 Chapter 4 Continuous Random Variables and Probability Distributions URL:  tml .

4-2 Probability Distributions and Probability Density Functions

Figure 4-3 Histogram approximates a probability density function.

0P X x because every point has zero width

Page 7: Engineering Statistics - IE 261 Chapter 4 Continuous Random Variables and Probability Distributions URL:  tml .

4-2 Probability Distributions and Probability Density Functions

Because each point has zero probability, one need not distinguish between inequalities such as < or for continuous random variables

Page 8: Engineering Statistics - IE 261 Chapter 4 Continuous Random Variables and Probability Distributions URL:  tml .

Example 4-2

SCILAB:-->x0 = 12.6;-->x1 = 100;-->x = integrate('20*exp(-20*(x-12.5))','x',x0,x1) x = 0.1353353

Page 9: Engineering Statistics - IE 261 Chapter 4 Continuous Random Variables and Probability Distributions URL:  tml .

4-2 Probability Distributions and Probability Density Functions

Figure 4-5 Probability density function for Example 4-2.

Page 10: Engineering Statistics - IE 261 Chapter 4 Continuous Random Variables and Probability Distributions URL:  tml .

Example 4-2 (continued)

SCILAB:-->x0 = 12.5;-->x1 = 12.6;-->x = integrate('20*exp(-20*(x-12.5))','x',x0,x1) x = 0.8646647

Page 11: Engineering Statistics - IE 261 Chapter 4 Continuous Random Variables and Probability Distributions URL:  tml .

4-3 Cumulative Distribution Functions

Definition

Page 12: Engineering Statistics - IE 261 Chapter 4 Continuous Random Variables and Probability Distributions URL:  tml .

4-3 Cumulative Distribution Functions

Example 4-4

Page 13: Engineering Statistics - IE 261 Chapter 4 Continuous Random Variables and Probability Distributions URL:  tml .

4-3 Cumulative Distribution Functions

Figure 4-7 Cumulative distribution function for Example 4-4.

Page 14: Engineering Statistics - IE 261 Chapter 4 Continuous Random Variables and Probability Distributions URL:  tml .

4-4 Mean and Variance of a Continuous Random Variable

Definition

Page 15: Engineering Statistics - IE 261 Chapter 4 Continuous Random Variables and Probability Distributions URL:  tml .

4-4 Mean and Variance of a Continuous Random Variable

Example 4-8


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