Solutions To Mathematics Textbooks/Probability and Statistics for Engineering and the Sciences (7th ed) (ISBN10: 0495382175)/Chapter 4
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< Solutions To Mathematics Textbooks  Probability and Statistics for Engineering and the Sciences (7th ed) (ISBN10: 0495382175)
Contents
Chapter 4  Continuous Random Variables and Probability Distributions[edit]
Section 4.1[edit]
Exercise 1[edit]
Given the density function
 Part a. Find
 Part b.
 Part c.
Exercise 2[edit]
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.