]. Chapter 3: 3[(e) {4,6}], 5[(a) 16, (c) 4], 9[I:
], 12[(a),(b) use Axiom 1 and Proposition 3.4.2]
Math 381 Probability and Statistics Spring, 2006
Meetings: TR 3:05-4:20, Engr 105 (NOTE CHANGE)
Instructor: Greg Morrow
Office: Engr 271, (719) 262-3184
E-mail: gjmorrow@math.uccs.edu
Hours: TR: 10:15-10:45, 2:00-2:50, or by appointment
Prerequisite: Calculus III (Math 235)
Text: Ross, Sheldon M. (2004) Introduction to Probability and Statistics for Engineers and Scientists, 3rd ed. San Diego, CA: Academic Press
Description: A calculus-based introduction to probability and statistics. Counting rules, independence, Bayes’ rule, random variables, expectation, discrete distributions including the binomial, geometric, Poisson, and hypergeometric distributions, the moment generating function, continuous distributions including the Uniform, Exponential, Normal, and Student distributions, joint and marginal distributions, expectation, covariance and correlation, law of large numbers and central limit theorem. Statistical studies include Chebyshev’s inequality, parameter estimation, confidence intervals, hypothesis testing, and normal approximation. The course covers some review from chapter 2 and chapters 3 through 8 of the text.
Homework and Tests: Homework will be assigned and collected each week; see the assignments and due dates on the syllabus below. In both homework and test problems all your steps must be documented independent of whether a calculator or other computing device is used. Late homework will not be accepted. The lowest homework score will be dropped. There will be two mid-semester tests and a final exam. Use of a calculator on tests is allowed but is limited to a scientific calculator. The following percentages may be used to compute the final grade: homework, 20%; test on 3.1-4.2, 25%; test on 4.3-4.6, 5.1-5.2, 25%; final test on 5.4-5.6, 6.1-6.4, 7.3-7.5 and 8.1-8.4, 30%.
Final Exam: Thursday, May 11, 1:40 pm – 4:10 pm
Grading: 90’s => grade of A , 80’s => grade of B or better, 70’s => grade of C or better.
Syllabus for Math 381, Spring 2006 (subject to change, revised 05/02/06)
1/17 – 1/19 2.3.2, 2.4, 3.1-3.5
1/24 – 1/26 3.6-3.8 Notes 1 and 2 HW I, Jan. 26
1/31 – 2/2 4.1, 4.2 Notes 3 HW II, Feb. 2
2/7 – 2/9 4.3, 4.4 HW III, Feb. 9
2/14 – 2/16 4.5; Notes 4 Test on 3.1-4.2, Feb. 16 HW IIIa DUE Feb. 14
2/21 – 2/23 4.6-4.7 , 2.6 Notes 5 HW IV, Feb. 23 Notes 6
2/28– 3/2 5.1, 5.2 Notes 7 HW V, Mar. 2
3/7– 3/9 5.4, 5.5 Review Test 2 HW VI, Mar. 9 Notes 8
3/14– 3/16 Test 2 on Mar. 16 :covers 2.6, 4.3-4.7, 5.1-5.2.
3/21 – 3/23 6.1-6.3 Notes 9 HW VII, Mar. 23
3/28-3/30 Spring Break
4/4 – 4/6 6.3.1, 6.3.2, 6.4 Notes 10 HW VIII, Apr. 11
4/11 – 4/13 6.5, 7.3.1, 7.4 Notes 11 HW IX, Apr. 18 CLT Simulation
4/18– 4/20 7.5, 8.1-8.3.2 Notes 12 HW X, Apr. 25 Review for Final
4/25 – 4/27 8.4.1,8.4.2 Notes 13 HW XI, May 2 Notes 14
5/2 – 5/4 Review Solution to Review for Final HW XII, May 11
5/11 Final Exam, Thursday May 11, 1:40-4:10 pm
Homework (HW).
III. Chapter 3: 33, 34, 36, 37 (a),(b) ((c) is extra), 39, 40. Chapter 4: 1, 2, 3. (NOTE CHANGE)
IIIa Chapter 4: 4, 6, 8.
IV. Chapter 4: 7, 9, 10, 13, 21, 22, 24, 25, 26, 27.
V. Chapter 2: 31. Chapter 4: 28, 30, 31, 32, 33, 34, 36, 39, 41, 44, 45, 53 (extra credit)
VI. Chapter 5: 1, 2, 3, 4, 5, 6, 10, 11, 12, 14, 15, 16, 18
VII. Chapter 5: 22, 23, 25, 26 (typo in part (b); see hints), 27, 28, 29 (extra credit), 31, 32. ((REST of Chp. 5 Problems MOVED)
VIII. Chapter 5: 34, 37, 38, 39; Chapter 6: 1(a) ((b) is extra credit), 2 (the sum ranges from 10 to 60, not 20 to 120), 3, 5, 6, 7 (Prob( X<=400), where X is the sum of the faces on 140 tosses).
IX. Chapter 6: 8, 9, 10, 11, 15, 21, 22.
X. Chapter 7: 9, 13, 14, 15, 20, 24, 27, 41, 42, 43
XI. Chapter 7: 53, 54, 55. Chapter 8: 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 17, 20.
XII. Chapter 8: 21, 27, 28, 29, 30, 33, 38, 39, 43, 55.
Short answers and hints to selected problems
I.
Chapter 2:
26[(a)]. Chapter 3: 3[(e) {4,6}], 5[(a) 16, (c) 4], 9[I:
], 12[(a),(b) use Axiom 1 and Proposition 3.4.2]
II.
Chapter 3: 17[use the algebraic identity 
], 18[Consider the sample space consisting of all sequences of
15 letters (labeled say b1-b5, and g1-g10). One may count the event in (a) by
first starting with the number of possibilities for the 4th letter,
and then multiplying by the succeeding numbers of possibilities for the
remaining letters in some specified order (say 5th, 6th,
…, 15th, 1st, 2nd, 3rd) . Ans.: (a)
1/3, (b) 1/3, (c) 1/15], 20[Ans.: 21/64; a sample space consists of all
four-letter words from an alphabet of the letters A, B, C, D. The event consists
of all four letter words with exactly two different letters, e.g. ABBA or CCCD],
23[consider a sample space of 6 equally likely outcomes; 3 of the outcomes are
in the given event], 25[(a) 2/5, (b) 1/26], 28[(c) 5/54], 29[(a) .785, (b)
16/43]
III.
Chapter 3: 34[(a) first compute P(Elevated) = 0.2281; then P(C|Elevated)=0.822
], 37[a parallel system consisting of two subsystems DOES NOT pass current if
and only if each subsystem does not pass current; also a series system DOES
pass current if and only if each component in the series passes current. Ans. to
(a): 
], 39[(a)1/4,(b)7/16, (c) 6/32] , 40[the
complementary event is the union
for the events A and B defined as follows. A: 0’s and 1’s
only occur. B: 0’s and 2’s only occur.]
Chapter 4: 1[.5,.2778,.1389,.0595,.0198,.0040], 4[(b)3/4,(c)1/12,(d)11/12,(e)1/6] 6[.3834, .6321].
IV. Chapter 4: 7[0.3292], 8[0.0183], 9[p(1,1)=3/10,p(1,2)=1/5,p(1,3)=1/10,p(2,1)=1/5,p(2,2)=1/10,p(3,1)=1/10],
10[(b) 12x^2/7+6x/7, (c)15/56], 13[(a) 2(1-x),0<x<1,(b) 2y,0<y<1], 24[A(p+.1)], 25[(b) 37], 26[(a) 2+2p(1-p)], 27[a=3/5,b=6/5].
V. Chapter 2: 29[ see Chebyshev’s inequality, pages 28-29], 31[use the definition, page 36]
Chapter 4:
28[2/a], 30[1/(n+1)], 31[68.28], 32[(a)164, (b) 21], 33[EX=EY=170/40], 36[
], 37[56.156], 39[(a)2.5, (b)1.25], 41[E=3/2, Var=3/4], 44[(a)
, 
. (b) E(X)=7/12, Var(X)=11/144], 45[(b) E(X1)=1.875,
Var(X1)=1.234, E(X2)=1.5, Var(X2)=.25, Cov(X1,X2)=.125].
VI. Chapter 5: 1[.8208], 2[.0579], 3[.2668], 5[p>2/3], 6[(a).0368 (b) 0]. 10[approx.(a) 1/(2e), (b) 1/e, (c) .0723],
11[(a) 
(b)
(c) 
]
12[.891], 14[(a) .451, (b) 1.000], 15[.0183]
18[0.3630].
VII. Chapter 5:
22[(a) 2/3, (b) 1/3], 23[(a) .798, (b)
.683], 25[ .0062], 26[(a) 9.6%, (b) typo; in part (b) 
is unknown . Ans.: 
], 27[L=1860],
31[P(X>4*10^6)=0.909], 32[Poisson approximation for p=0.0228 and n=100; prob=.197], 34[(a).415, (b).381, (c).356], 37[(a).135, (b).368], 38[.287], 39[.368, (b) 1/3].
VIII. Chapter 6: 3[0.042], 5[(a) 0.9906], 6[0.1436], 7[~0],
IX. Chapter 6: 10[0], 11[(a) .266, (b) .1056, (c) .0304, (d) .0062], 15[ .148], 21[.5588], 22[(a) .671, (b) .6915, (c) .903, (d) 1].
X. Chapter 7: 9[ (a) 11.48+-.0496], 14[1.2+-.128]
XII. Chapter 8: 21[ p=.142], 28[p=.4238], 43[We find that for a one-sided alternative, p>.10, (in fact p=.123)], 55[(a) z=1.2; fail to reject H0, (d) z=2.31 & p=.01; reject H0].