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

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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]


  • 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.