Solutions To Mathematics Textbooks/Probability and Statistics for Engineering and the Sciences (7th ed) (ISBN-10: 0-495-38217-5)/Chapter 4

< Solutions To Mathematics Textbooks‎ | Probability and Statistics for Engineering and the Sciences (7th ed) (ISBN-10: 0-495-38217-5)

Contents

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.