Homework 7 Answers

BSTA 550

Modified

November 12, 2024

Chapter Turn In Extra Problems
28 TB # 1, 10
291 NTB # 1-2 TB # 10, 14, 23, 26, 11, 13, 32
31 TB # 18 TB # 13, 14, 17
32 TB # 8 TB # 3, 5, 102, 15
33 NTB # 3 TB # 3, 9, 10
35 TB # 10, NTB # 4 TB # 6, 9, 24

Non-textbook problems

  • #1: See class notes for starting!

  • #2:

    1. \(E(V) = 87850 \text{ ft}^3\), \(\text{Var}(V) = 19100116 \ (\text{ft}^3)^2\)

    2. Expected value correct, variance incorrect

  • #3:

    1. \(1 - e^{-1}\)

    2. 0.0008216

  • #4: 0.001998

Textbook problems

There are answers at the back of the book!! Selected answers (or hints) not provided at the end the book:

  • Chapter 28

    • # 10: (a) 8/9     (b) 14/3     

    • # 18: 4/5

  • Chapter 29

    • # 10: (a) 26/81     (b) 74/9

    • # 14: (a) 67/3     (b) 1/14     (c) 25/12     (d) \(\sqrt{25/12}\)

    • # 26: 250

    • # 32: See notes (or book) for the proof from the discrete random variables case. The proof doesn’t depend on what type of random variable (discrete vs. continuous) is being used.

    • NTB # 3: (a) 63     (b) 287/3     (c) -1, 41/3     (d) -7, 287/3

  • Chapter 31

    • 14.
        1. 0.25
        1. 0.02887
        1. 0.063
        1. 0.0145
        1. 0.01625
        1. 0.0055
        1. 6.195
        1. 0.00433
        1. 61.95
        1. 0.0433
    • 17. 2.25
    • 18. \(\frac{7}{15}\)

  • Chapter 32

    • 8. 0.2526
    • 5. 0.8047
    • 10. 0.4323

  • Chapter 33

    • 10.
        1. \(f_x(x) = \frac{x}{9} e^{-x/3}\) for \(x > 0\)
        1. 0.4963

  • Chapter 35

    • 6.
        1. 0
        1. -1.13
        1. \(\pm 0.32\)
    • 10.
        1. 0.0475
        1. 0.0475
        1. 0.2283
        1. 68.97 to 81.03
        1. 48 to 102
        1. 68.97
    • 24.
        1. 0.2119
        1. 0.0011
    • NTB Parachute Reference: 0.002

Footnotes

  1. I recommend doing the Chapter 29 Extra Problems in the order listed.↩︎

  2. Assume \(X\) and \(Y\) are independent.↩︎