Download 4-8 Exponential Distribution

Engineering Statistics - IE 261
Chapter 4
Continuous Random Variables and
Probability Distributions
URL:
http://home.npru.ac.th/piya/ClassesTU.h
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http://home.npru.ac.th/piya/webscilab
4-1 Continuous Random Variables
current in a copper wire
length 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.
P  X  x   0  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