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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
4-1 Continuous Random Variables
current in a copper wirelength of a machined part
Continuous random variable X
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.
4-2 Probability Distributions and Probability Density Functions
Figure 4-2 Probability determined from the area under f(x).
4-2 Probability Distributions and Probability Density Functions
Definition
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
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
Example 4-2
SCILAB:-->x0 = 12.6;-->x1 = 100;-->x = integrate('20*exp(-20*(x-12.5))','x',x0,x1) x = 0.1353353
4-2 Probability Distributions and Probability Density Functions
Figure 4-5 Probability density function for Example 4-2.
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
4-3 Cumulative Distribution Functions
Definition
4-3 Cumulative Distribution Functions
Example 4-4
4-3 Cumulative Distribution Functions
Figure 4-7 Cumulative distribution function for Example 4-4.
4-4 Mean and Variance of a Continuous Random Variable
Definition
4-4 Mean and Variance of a Continuous Random Variable
Example 4-8