MAT 2210 (Elementary Probability & Statistics), CRN 10185, Section 001
and
MAT 6150 (Probability & Statistics for Teachers), CRN 12174, Section 001
Fall 2006
Professor Drucker

ASSIGNED EXERCISES

(last updated December 12, 2006)

Text: Robert V. Hogg and Elliot A. Tanis, Probability and Statistical Inference (Seventh Edition), Pearson Prentice Hall, 2006.

ADVICE: Do these assignments as we come to them. Solve extra problems when you have trouble with a topic. Note that the answers to odd-numbered computational exercises are given at the back of the text. Don't look at the answers until you've completed the exercises. Working backwards from the answers leads to bad habits. Your goal should be to develop confidence in your problem-solving skills and find ways to check your work other than looking at the answers.
Chapter 1. Probability
1.1 #1, 3, 7, 11, 13
1.2 #1, 3, 5, 7, 13, 15
1.3 #1, 3, 5, 7, 13, 17, 19
1.4 #1, 3, 5, 7, 9, 11, 15, 17
1.5 #1, 3, 5, 7, 9, 11, 15ab, 16 [Answer to 16. a. 5/9 b. 3/5]
1.6 #1, 2, 5, 6, 9 [Answers. 2. a. 0.79 b. 0.43   6. 0.659, 0.264, 0.077]
Chapter 2. Discrete Distributions
2.1 #3, 6a, 7a, 8a, 10, 14 [Answers. 6a. ƒ(x) = (6 – | 7 – x | ) / 36.   8a. ƒ(w) = 1/12 for all w.   10. a. 39/98   b. 221/245]
2.2 #1, 3, 4, 5, 7, 14 [Answers. 4. 0, 8/9, 20/3   14. a. 50   b. ƒ(x) = 0.4 for x = 25, ƒ(x) = 0.3 for x = 100 or 300.   c. 130]
2.3 #2, 3, 7a, 13, 16, 18ab [Answers. 2. a. 3/4, 9/16   b. 2, 1   16. a. 1.333   b. 1.275   18. a. 3, 19, 16, 9   b. 0.87]
2.4 #2, 4, 6, 8, 10, 11, 13
   [Answers. 2. ƒ(–1) = 11/18, ƒ(1) = 7/18, μ = – 4/18, σ2 = 77/81.   4. a. 0.5269   b. 0.4731   c. 0.1490   d. σ = 1.723
    6. a. b(7, 0.15)   b. i. 0.2834 ii. 0.3960 iii. 0.9879   8. a. b(15, 0.2)   b. μ = 0.3 σ2 = 2.4 σ = 1.549   c. 0.1642   10. a. b(6, 0.05)
    b. 0.3, 0.285   c. i. 0.7351 ii. 0.9672 iii. 0.0328]
2.6 #1, 2, 4, 6, 8, 9, 10
   [Answers: 2. 0.224   4. 0.134   6. 0.607   8. a. 0.040   b. 0.497   10. 0.938]
Chapter 3. Continuous Distributions
3.1 #1, 2, 3, 17 [Answers: 2. 3.58, .5116]
3.2 #1c, 2, 4, 8a, 9ab
   [Answers: 2. a. c = 2, F(x) = 0 on (–∞, 0), x4/16 on [0, 2), 1 on [2, ∞)   b. c = 2, F(x) = 0 on (–∞, –2), x/16 + 1/2 on [–2, 2),
    1 on [2, ∞)   c. c = 1/2, F(x) = 0 on (–∞, 0), sqrt(x) on [0, 1), 1 on [1, ∞)   4. a. 8/5, 0.1067, 0.3266   b. 0, 12/5, 1.5492  
    c. 1/3, 4/45, 0.2981   8. a. c = 1]
3.3 #3, 6abc, 8, 10 [Answers: 6. a. e–1/2 – e–3/2   b. e–3/2   c. e–3/2   8. a. &fnof(x) = (2/3)e–2x/3, 0 ≤ x ≤ ∞   b. e–4/3   10. a. e–2   b. e–2]
3.4 #9, 10, 11 [Answer: 10. a = 5.226, b = 21.03]
Chapter 4. Multivariate Distributions
4.1 #1, 3bcde, 7
4.2 #1, 3ab, 7
4.5 #1, 2, 4, 8, 9, 11   [Answers: 2. a. 15/256   b. 1/32   4. a. 0.036   0.125   8. a. 27/1024   b. 81/512   c. (15/16)3]
4.6 #1, 2, 3a, 5, 17ac, 18ab
    [Answers: 2. 1, 1/10   18. a. P(W = w) = ( 4 – | 5 – w | ) / 16   P(U = u) = &fnof(u) / 256, where &fnof(u) = 1 if u = 4 or 16,
    &fnof(u) = 4 if u = 5 or 15, &fnof(u) = 10 if u = 6 or 14, &fnof(u) = 20 if u = 7 or 13, &fnof(u) = 31 if u = 8 or 12,
    &fnof(u) = 40 if u = 9 or 11, and &fnof(u) = 44 if u = 10.]
Chapter 5. The Normal Distribution
5.2 #1, 2, 4, 5, 7, 9, 14, 19, 20, 25
   [Answers: 2. a. 0.3078   b. 0.4959   c. 0.2711   d. 0.1646   e. 0.0526   f. 0.3174   g. 0.0456   h. 0.0026  
    4. a. 1.282   b. –1.645   c. –1.66   d. –1.82   14. a. 0.0401   b. 0.8159   20. a. 0.7324   b. 0.0606   c. 0.2912]
5.3 #1, 3–6, 8b, 9, 11, 14
   [Answers: 4. a. 0.05   b. 0.9916   c. 0.0122   6. a. 0.900   b. 0.900   8. b. 0.8790
    14. a. μ = 24.5, 21.3; σ2 = 1.805, 0.91125   b. N(3.2, 2.716)   c. 0.9738]
5.4 #1–4, 5b, 6–9, 12, 15
   [Answers: 2. 0.2313   4. 0.6853   6. a. 2/3, 2/9   b. 0.4332   8. a. 24.43   b. 0.0733   c. 0.7566   12. 0.3085]
5.5 #4–11, 14, 16, 21, 22
   [Answers: 4. 0.6247   6. 0.0668   a. 0.10   b. 0.0668   c. 0.6247   10. 0.4385   14. a. 0.2417   b. 0.220   c. 0.2244
    16. a. 0.4186   b. 0.5714   c. 0.5642   22. a. Poisson with mean 30   b. 0.2056]
Chapter 6. Estimation
6.1 #2, 6, 7
   [Answers: 2. a. sample mean = 4/3   b. sample variance = 88/69
    6. b. min = 310, 1st quartile = 390, median = 405, 3rd quartile = 422.5, max = 480.
    d. IQR = 32.5, so we draw inner fences at 356.25 and 453.75 and outer fences at 307.5 and 502.5.
    There are no outliers, but 310, 325, 460, 463, 470, 475 (twice), and 480 are suspected outliers.]
6.2 #4a, 12abc  [Answers: 4. a. 394 / 7,   5452 / 97   12. d. 1/(n–1)]
6.4 #2, 4–7, 9, 11, 12ab, 14a
   [Answers: 2. a. [77.272, 92.728]   b. [79.12, 90.88]   c. [80.065, 89.935]   d. [81.154, 88.846]
    4. a. 56.8   b. [55.56, 58.04]   c. 0.0082   6. [8.15, 15.75]   12. a. 3.58   b. 0.512   14. a. [232.707, 258.893] ]
6.5 #1, 2, 5, 6a, 8a, 9
   [Answers: 2. [–74.517, 63.667]   6. a. [–115.480, 129.105]   8. a. [0.7653, 1.2747] ]
6.6 #1, 2, 3abc, 9–12
   [Answers: 2. a. 1.858   b. [1.255, 3.560] or [1.131, 3.246]   c. [1.335, 3.179] or [1.202, 2.894]   10. [0.383, 0.976]
    12. a. Use F0.025(13, 13) = 3.115 to get [0.589, 5.719]   b. [0.77, 2.39] ]
6.7 #2–4, 6, 9, 11–16
   [Answers: 2. [0.66, 0.76]   4. [0.6746, 0.7257]   6. [0.247, 0.273]   12. a. 0.793   b. [–0.306, –0.179]
    14. a. 0.144   b. [0.095, 0.194]   c. 0.076   d. [0.024, 1]   16. [0.011, 0.089] ]
6.8 #1, 2, 4, 6, 7, 10, 12–14
   [Answers: 2. 289   4. 537   6. 175   10. 404   12. 482   14. 1885 (1884 if you use p = 0.680 rather than
    p = 686/1009 ≈ 0.679881) ]
Chapter 8. Tests of Statistical Hypotheses
8.1 #3, 5, 6ab, 8, 11, 12, 15, 17, 19, 20
   [Answers: 6. a. z ≤ –1.645   b. z = –2.05; reject H0   8. a. z = –2.280 < –2.326; don't reject H0   c. p-value = 0.0113
    12. a. critical region: z ≥ 1.96   b. z = 2.054   c. p-value = 0.0200 < 0.025, so reject H0   d. [0.659, 1]
    20. a. z ≥ 1.645   b. z = 2.341; reject H0   d. p-value ≈ 0.0096]
8.2 #1–3, 5, 7, 8, 11, 13, 15, 19, 21
   [Answers: 2. a. t =3 > 1.753, so reject H0   b. p-value ≈ 0.005   8. a. critical region: t ≥ 2.764   b. t = 0.699; do not reject H0
    c. p-value ≈ 0.25  d. critical region: χ2 ≤ 3.940   e. χ2 = 4.104; don't reject H0   f. 0.05 < p-value < 0.10]
8.3 #1ab, 2abc, 3ab, 5abc, 6abc, 7
   [Answers: 2. a. critical region: t ≤ 2.473   b. t = 5.570; reject H0   c. Accept assumption of equal variances
    6. a. critical region: | t | ≥ 2.101   b. | t | = 2.101; reject H0   c. 0.01 < p-value < 0.05]
8.5 #2, 4, 7, 8
   [Answers: 2. q4 ≈ 3.784 < χ20.10(4), so don't reject H0   4. q4 = 4.95 < χ20.05(4), so don't reject H0   8. q3 ≈ 6.368 < χ20.05(3),
    so don't reject H0;   0.05 < p-value < 0.10;   interval ≈ [0.297, 0.373] ]

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