Math 477-02 - Solutions to Review problems for Exam #2 - April 15, 2009
Review Session: Monday, April 13, 6:30-8:30 M in SEC-211 (BUSCH)
Calculators may not be used on the exam. You will be given a sheet containing a copy
of table 5.1 of the the text and
Homework Assignment 1 Solutions
Math 477 Sections 01,04
January 27, 2012
1
Problems
5.) Since there are 8 choices for the rst digit, 2 choices for the middle digit,
and 9 choices for the nal digit, the number of area codes is
8 2 9 = 144.
If we restrict t
640:47702
SPRING 2017
SOLUTIONSASSIGNMENT 6
Chapter 3. Problems: p. 101 #49a. The events are: C: has cancer; H healthy; Y : test says cancer.
P (C|Y ) =
P (Y |C)P (C)
(.268)(.7)
=
.
P (Y |C)P (C) + P (Y |H)P (H)
(.268)(.7) + (.135)(.3)
p. 102 #55. Suppose
640:47702
SPRING 2017
SOLUTIONSASSIGNMENT 9
Chapter 4. p. 165 #27. Let IE be the indicator function of E; then X = A IE + C is the random
variable that gives their profit. Thus we need 0.1 A = E[X] = A p + C or C = (0.1 + p) A as
the cost of the policy to
640:47702
SPRING 2017
SOLUTIONSASSIGNMENT 8
Chapter 4. Problems: p. 164 #19. The size of the jump in F at a point gives the probability
that X takes that valuei.e., probability mass function at that point. At other places the
probability mass function is
640:47702 SPRING 2017
SOLUTION SASSIGNMEN T 3
Chapter 2. Problems: p. 48 #8. a) .8 b) .3 c) 0
p. 48 #9. 74%
p. 48 #10. If R is the event of wearing a ring and N is the event of wearing a necklace, then
P(RcNc)=0.6so P(RUN)= P(Rc NC)C ) 21 0.6204. SinceP(R
640:47702
SPRING 2017
SOLUTIONSASSIGNMENT 1
Chapter 1. Problems: p. 15 #1. The first two places can be chosen in 26 26 ways and the last 5 in
10 10 10 10 10 ways; the product is 6.76 108 . With no repetitions, the choices would number
26 25 10 9 8 7 6 1.9
640:47702
SPRING 2017
SOLUTIONSASSIGNMENT 7
Chapter 3. Problems: p. 105 #81. This is gamblers ruin with n = 30, i = 15 and p = 0.55, so the
1
1 (0.45/0.55)15
=
0.953026559 .
probability of winning is
30
1 (0.45/0.55)
1 + (9/11)15
p. 105 #82. (a) Let Sk d
640:47702
SPRING 2017
SOLUTIONSASSIGNMENT 2
Chapter 2. Problems: p. 48 #1. S = cfw_RR, RG, RB, GR, GG, GB, BR, BG, BB
S = cfw_RG, RB, GR, GB, BR, BG
p. 48 #2. A typical point in the sample space might look like 5 1 3 5 5 2 6; this means that we
rolled the
640:47702
SPRING 2017
SOLUTIONSASSIGNMENT 10
Chapter 4. Problems: p. 166 #40. The number X of correct answers is a binomial random variable
with parameters (5, 1/3), since the probability of a correct guess on any question is 1/3. Thus
4 5
11
5
1
2
5
1
=
640:47702
SPRING 2017
SOLUTIONSASSIGNMENT 5
Chapter 3. Problems: p. 97 #1. Let E be at least one 6, F be different numbers. There
are 36 outcomes, 6 in which the two dice are the same and hence 30 in which they are different,
so P (F ) = 30/36 = 5/6. Ther
640:47702
SPRING 2017
SOLUTIONSASSIGNMENT 4
Chapter 2. Problems: p. 49 #15. For all of these problems,
we must count the number of ways to
choose the type of hand in question, then divide by 52
to
find
the probability.
5
4
13
(a) There are 4 = 1 ways to c
ASSIGNMENT 3
DUE FRIDAY 13TH 2015
MATH 477
As usual please explain your reasoning to receive full credit. The homework is a
bit lighter than usual, since we will also cover some of this material in more depth
on Tuesday (and in general there are several n
MATH 477
ASSIGNMENT 2
DUE FRIDAY, FEBRUARY 6
Each question is worth 10 points. Not all questions are of equal diculty. The
grading takes into account both the reasoning and the correctness of the answer. To
obtain more than half of the points it is import
Homework Assignment 2 Solutions
Math 477 Sections 01,04
February 1, 2012
1
Problems
4b) In this experiment, A, B, and C repeatedly ip a coin. The rst person
to get heads is the winner. So, assign 0 for each loss (coin lands on tails)
and 1 for a win (coin
Homework Assignment 3 Solutions
Math 477 Sections 01,04
February 12, 2012
1
Problems
1.) Let S be the event that we roll at least one six, and D be the event
that the dice land on dierent numbers. The easiest way to compute this
probability is to directly
Homework Assignment 4 Solutions
Math 477 Sections 01,04
February 26, 2012
1
Problems
28.) We know that the rst ace is the 20th card in the deck. Thus, the rst 19
cards are all non-aces. Among the last 32 cards, there are 3 aces and 29
non-aces.
(a) Let A2
Homework Assignment 5 Solutions
Math 477 Sections 01,04
March 2, 2012
1
Problems
4) Let X be the highest rank achieved by a woman. Clearly X cfw_1, 2, 3, 4, 5, 6
since X = 7 or higher is impossible (there are 5 women and 5 men and
so the lowest rank a wom
Homework Assignment 6 Solutions
Math 477 Sections 01,04
March 22, 2012
1
Chapter 4 Problems
31) Let the random variable S be the score the meteorologist receives. Let
p be the probability of rain the meteorologist chooses to broadcast (and
which determine
Homework Assignment 7 Solutions
Math 477 Sections 01,04
March 31, 2012
1
Chapter 5 Problems
16) We will assume that the rainfall in one year is independent of the rainfall
in any other year. This is certainly not something thats obviously true
(in fact, I
Homework Assignment 8 Solutions
Math 477 Sections 01,04
April 10, 2012
1
Chapter 6 Problems
1.) (a) X is the larger value on either die and Y is the sum of the values.
Clearly, X cfw_1, 2, 3, 4, 5, 6 while Y is between 2 and 12. We illustrate the computat
Homework Assignment 9 Solutions
Math 477 Sections 01,04
April 28, 2012
1
Chapter 6 Problems
40.) (a) To compute the conditional mass function for X given Y , we rst
need the marginal mass function for Y :
pY (1) = p(1, 1) + p(2, 1) =
1
,
4
pY (2) = p(1, 2
Homework Assignment 9 Solutions
Math 477 Sections 01,04
May 1, 2012
1
Chapter 7 Problems
75.) From the m.g.f.s, we recognize that X is Poisson with = 2, and Y is
binomial with n = 10 and p = 3/4 (using the 1-1 correspondence between
distributions and gene
Math 477-02 - REVIEW PROBLEMS FOR FINAL EXAM - April 2009
REVIEW SESSION: WEDNESDAY, MAY 6, 4-7 PM in ARC-110 (BUSCH)
Calculators may not be used on the exam. You will be given a sheet containing a copy
of table 5.1 of the the text and the following formu