Solutions To Mathematics Textbooks/Probability and Statistics for Engineering and the Sciences (7th ed) (ISBN10: 0495382175)/Chapter 4
< Solutions To Mathematics Textbooks  Probability and Statistics for Engineering and the Sciences (7th ed) (ISBN10: 0495382175)Chapter 4  Continuous Random Variables and Probability DistributionsEdit
Section 4.1Edit
Exercise 1Edit
Given the density function
 Part a. Find
 Part b.
 Part c.
Exercise 2Edit
Let
 Part a.
 Part b.
 Part c.
 Part d. For , compute
Exercise 3.Edit
Let be a probability density function.
 Part a. graph
 Part b.
 Part c.
 Part d.
Exercise 4.Edit
Let have the Rayleigh distribution with the probability density function
 Part a.
Verify that is a pdf.

 First notice that for all
 Next show the integral over the whole number line equals one:
 Part b. Let .
 Probability is at most 200

 Probability is less than 200

 Probability is at least 200
 The probability is between 100 and 200 assuming .
 Give an expression for , i.e., define the cumulative distribution function.