Engineering Statistics - IE 261

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

2. 4-1 Continuous Random Variables current in a copper wire length of a machined part  Continuous random variable X

3. 4-2 Probability Distributions and Probability Density Functions Figure 4-1Density 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 totalloading between points a and b is determined as the integral of the density function from a to b.

4. 4-2 Probability Distributions and Probability Density Functions Figure 4-2Probability determined from the area under f(x).

5. 4-2 Probability Distributions and Probability Density Functions Definition

6. 4-2 Probability Distributions and Probability Density Functions Figure 4-3Histogram approximates a probability density function.  because every point has zero width

7. 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

8. Example 4-2 SCILAB: -->x0 = 12.6; -->x1 = 100; -->x = integrate('20*exp(-20*(x-12.5))','x',x0,x1) x = 0.1353353

9. 4-2 Probability Distributions and Probability Density Functions Figure 4-5Probability density function for Example 4-2.

10. 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

11. 4-3 Cumulative Distribution Functions Definition

12. 4-3 Cumulative Distribution Functions Example 4-4

13. 4-3 Cumulative Distribution Functions Figure 4-7Cumulative distribution function for Example 4-4.

14. 4-4 Mean and Variance of a Continuous Random Variable Definition

15. 4-4 Mean and Variance of a Continuous Random Variable Example 4-8