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 | edit source]Section 4.1
[edit | edit source]Exercise 1
[edit | edit source]Given the density function
- Part a. Find
- Part b.
- Part c.
Exercise 2
[edit | edit source]Let
- Part a.
- Part b.
- Part c.
- Part d. For , compute
Exercise 3.
[edit | edit source]Let be a probability density function.
- Part a. graph
- Part b.
- Part c.
- Part d.
Exercise 4.
[edit | edit source]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.