HW 1: Solutions 2.3. a. Event A = cfw_ SSF, SFS, FSS b. Event B = cfw_ SSS, SSF, SFS, FSS c. For Event C, the system must have component 1 working ( S in the first position), then at least one of the other two components must work (at least one S in the
Chap 4: Continuous RV
Continuous RV can take on any number an interval. (Not isolated values like discrete case) X= height to nearest inch is discrete; Y = true height is continuous. U = time till failure of a product is continuous.
1
Sect. 4.1: pdf s Pr
NAME: Solution to Midterm-1, SP2011
(10 x 4 = 40 points)
Question 1
Special Instructions for this question: You DO NOT have to show work for (a) through (e).
Write the correct choice (A/B/C/D) inside the box on the right hand side. Any scratch work will
n
NAME: SOLUTION to Midterm II_
STAT 427
Prof. Goel
Midterm II
Spring, 2007
MWF 9:30 - 10.20
Problem 1. [10 points] A gas station has two islands: Island #1 has six pumps, and Island #2 has
four pumps. Let the random variables X and Y denote:
X = number of
Statistics 427: Sample Final Exam
Instructions: The following sample exam was given several quarters ago in Stat 427. The
same topics were covered in the class that year. This sample exam is meant to be representative of the types of questions that might
Review Questions for Midterm 2
Review Set 1
1
2
3
(c)
4
5
6
Review Set 2
7
8
9
10
11
Answer Key
These are just the final answers and not complete solutions. To get full credits,
you will have to show the complete solutions.
Review SET 1
Review SET 2
1 The
Stat 427
NAME_
Exam 2
Professor Berliner; WI 2011
Exam Score: _/100 points
Part I Score: _/40 points
Fill-in the blanks: Each question is worth 5 points (no partial credit)
For problems 1 through 4, let Z be a standard normal RV and find
1. P(1.00 < Z < 2
Stat 427
NAME_solutions_
Exam 1
Professor Berliner; WI 2011
Exam Score: _/100 points
Part I Score: _/40 points
Fill-in the blanks: Each question is worth 4 points (no partial credit)
1. The _sample space_ of an experiment is the set of all possible
outcom
Statistics 427-SP 2011
Midterm II - Solution
Note: Answers to all versions of a question are provided here.
Question 1 (6x2.5 points)
Special Instructions for this question: You DO NOT have to show work for (a) through (e).
Just fill in the blanks. Any sc
Solution
Homework Assignment # 1
SP 2011
Dr. Goel
A1 cfw_ A2 A3
Note that the above event can also be expressed as
[ A1 cfw_A2 A3 ] [ A2 cfw_A1 A3] [ A3 cfw_A1 A2 ]
Remark for d: you may calculate P(at most two errors)=P(no error)+P(1 error)+P(2
errors)
STAT 427
Home Work Assignment #2
Dr. Goel
Solution
Spring 2011
REMARK:
In part c, P exactly one P( A1
A2 '
A3 ') P( A1 '
A2
A3 ') P( A1 '
A2 '
A3 )
E. P(M| SS)= P(M and SS)/P(SS)
=(.08+.07+.12)/( .08+0.07+0.12+0.04+0.02+0.05+0.03+0.07+0.08)
=0.27/0.56=0.5
Solution
Homework Assignment # 3- Chapter 3
6.
SP 2011
Dr. Goel
Possible X values are 1, 2,(all the positive integers)
Possible samples: S1=(L) each with X=1; S2=(RL,or AL) each with X=2;
S3=(RRL, RAL, ARL, AAL) each with X=3 and
S4=(RRAL, RAAL, AARL, RAR
Solution
SP 2011
Homework Assignment # 4- Chapter 3
Dr. Goel
30.
36.
Let H(X) denote the possible payment by the company, then
EH ( X ) 0 0.8 0.1 (1000 500) 0.08 (5000 500) 0.02 (10000 500) 50 360 190 600
Thus, in order to maintain the expected profit to
Solution
SP 2011
Homework Assignment # 5- Chapter 3 and 4
Dr. Goel
3.68
3.82
3.86:
4.2
d, if k>-5 and k+4<5, i.e, -5<k<1, then
P(k X k 4)
k 4
k
1
dx 0.4
10
If k<-5, then P(k X k 4)
k 4
5
1
k 9
dx
10
10
1
5k
dx
k 10
10
P(k X k 4)
If k>1, then,
5
4.4
(
Solution
SP 2011
Homework Assignment # 6- Chapter 4
Dr. Goel
Remark: When calculating P(X<A), where X follows a normal distribution with mean=a, std=b,
the formula is P(X<A) = P(X-a)/b<(A-a)/b). Since (X-a)/b follows the standard Normal(0,1),
P(X<A) = P(Z
Solution
SP 2011
Homework Assignment # 7- Chapter 5
Dr. Goel
1.
a.
P(X = 1, Y = 1) = p(1,1) = .20
b.
P(X 1 and Y 1) = p(0,0) + p(0,1) + p(1,0) + p(1,1) = .42
c.
At least one hose is in use at both islands.
P(X > 0 and Y > 0) = p(1,1) + p(1,2) + p(2,1)
+ p
Stat 427 HW 1 (25 pts)
Name_
Please read and follow the information in the Homework Policies document posted in the
Homework section of Carmen. Its your responsibility to know how to avoid academic misconduct.
Please read and follow the conditions for f
NAME: _
STAT 427
Prof. Goel
Midterm I
Spring, 2007
MWF 9:30 - 10.20
REMARKS:
This is a closed book examination. However, you are allowed to use your own
calculator as well as two (8.5 x 11 two-sided) crib-sheets.
There are four problems worth a total of
CHAPTER 7
Section 7.1
1. a.
z 2 = 2.81 implies that 2 = 1 - (2.81) = .0025 , so = .005 and the confidence
level is 100 1 -
(
)% = 99.5% .
b. c.
z 2 = 1.44 for = 2[1 - (1.44)] = .15 , and 100(1 - )% = 85% .
99.7% implies that
= .003 , 2 = .0015 , and z .0
CHAPTER 6
Section 6.1
1. a. We use the sample mean,
x to estimate the population mean .
^ =x=
b.
xi 219.80 = = 8.1407 n 27
We use the sample median, ascending order).
~ = 7.7 (the middle observation when arranged in x
1860.94 - ( 219.8) 27 s = = 1.660 26
HW 2 Solutions: All from Chapter 2 45. a. b. P(A) = .106 + .141 + .200 = .447, P(C) =.215 + .200 + .065 + .020 = .500 P(A C) = .200
P( A C ) .200 .400 . If we know that the individual came from ethnic group 3, the P(C ) .500 P( A C ) .200 .447 . If a pers
HW 3: Solutions All are from Chapter 3 12.
b. c.
a. In order for the flight to accommodate all the ticketed passengers who show up, no more than 50 can
Using the information in a. above, P(Y > 50) = 1 - P(Y 50) = 1 - .83 = .17 For you to get on the flight
CHAPTER 8
Section 8.1
1. a. b. c. d. Yes. It is an assertion about the value of a parameter. No. The sample median
~ X is not a parameter.
No. The sample standard deviation s is not a parameter. Yes. The assertion is that the standard deviation of populat
CHAPTER 9
Section 9.1
1. a.
E (X - Y ) = E( X ) - E (Y ) = 4.1 - 4.5 = -.4 , irrespective of sample sizes.
V ( X - Y ) = V (X ) + V (Y ) =
of
2 12 2 (1 .8) (2.0) = .0724 , and the s.d. + = + m n 100 100 2 2
b.
X - Y = .0724 = .2691 .
c.
A normal curve wit
CHAPTER 10
Section 10.1
1. a. Ho will be rejected if
f F.05, 4,15 = 3.06 (since I 1 = 4, and I ( J 1 ) = (5)(3) = 15 ).
The computed value of F is
f =
3.06 , Ho is not rejected. The data does not indicate a difference in the mean tensile strengths of the
CHAPTER 11
Section 11.1
1. a.
30.6 59.2 7.65 = 7.65 , MSE = = 4.93 , f A = = 1.55 . Since 1.55 is 4 12 4.93 not F. 05, 4 ,12 = 3.26 , don't reject HoA . There is no difference in true average tire MSA =
lifetime due to different makes of cars.
b.
44.1 14.
CHAPTER 12
Section 12.1
1. a. Stem and Leaf display of temp: 17 0 17 23 17 445 17 67 17 18 0000011 18 2222 18 445 18 6 18 8
stem = tens leaf = ones
180 appears to be a typical value for this data. The distribution is reasonably symmetric in appearance and
CHAPTER 13
Section 13.1
1. a.
2 ^i is 10 1 - 1 - (x i - 15 ) = = 250 , so s.d. of Yi - Y 5 250
x = 15
and
(x
j
- x)
2
6.32, 8.37, 8.94, 8.37, and 6.32 for i = 1, 2, 3, 4, 5. b. Now
x = 20 and
(x
i
- x ) = 1250 , giving standard deviations 7.87, 8.49, 8.