Stat 321 – HW 5

Due Tuesday, Feb. 19

Reminders: Solutions to this assignment will be posted Tuesday night. Additional review problems and solutions will be posted this weekend. Exam 2 will be Thursday, Feb. 21.

In the following problems, clearly define the events of interest in terms of “X” and explain your calculations. If you use technology to evaluate integrals, make sure you still show the set up of the integration (e.g., limits, proper dx notation, etc.)

1) Exercise #6 (p. 135)

2) Using the pdf given in exercise #22 (p. 144), answer the following questions:

(a) Provide a well-labeled and scaled sketch of f(x) vs. x (ideally using a computer)

(b) Determine the expression for the cdf F(x), for all values of x, and provide a rough sketch of F(x) vs. x

(c) Use the F(x) you found and determine the median of X by setting F(x) = .5 and solving for x.

(d) Use the F(x) you found and determine the 75^th percentile of X. Hint: Proceed as in (d) but think about what you want to set F(x) equal to.

(e) Determine E(X).

(f) How do the mean E(X) and the median from (c) compare? Does the relationship make sense based on your graph in (a)?

3) Exercise #34 (p. 154)

4) Exercise #38 (p. 155)

5) Exercise #66 (p. 162)

You might want to pick some odd-numbered problems from section 4.5 for additional practice.