MATHEMATICS 231
Test 1, Thursday, Oct 4, 2012
Name:
(Please print.)
Please circle your section number and the time your class meets.
Section 010
MWF 9:10a
Section 011
TR 2:35p
This is a closed book exam. You may use a calculator, however, in Part II, you
Homework-014
64. Assume that the lifetime of a certain component has an exponential distribution with mean
3. Find all of the following: the value of the parameter, f , the 55th percentile and the
standard deviation of lifetimes, the probability that a co
Mathematics 231 Solution to Problems #68-70, plus S1
X
P (66.4 < X < 75.3)
(68) SOLUTION TO PROBLEM 68: We let
For (a), we are to nd
be the height of a male chosen at random, so,
(since
X
X N (70, 3.12 ).
is a continuous random whose density function has
1
MATH 231
Spring, 2014
Assigned Problems- Part II
(Note that the numbering of exercise refers to the 3rd edition of the textbook)
48. A sample of 7 widgets is chosen at random from an enormous lot of widgets in which it is
known that 18% are defective. F
MATHEMATICS 231
Practice Test 1
THIS IS AN ACTUAL TEST 1 FROM A RECENT, BUT UNSPECIFIED OFFERING OF MATHEMATICS 231.
The format of the test is similar to the format of our test (6 short answer,
no partial credit questions followed by 3 regular problems wh
Mathematics 231 Solution to Problems #71-72
(71) SOLUTION TO PROBLEM 71: From the assumption that the lifetime, X , (measured in years) of a
randomly selected component has an exponential distribution (with parameter ), we know that X = X =
1
1
, and so,
Mathematics 231 Solution to Problems #73-75,S2,77-79
(73) SOLUTION TO PROBLEM 73: Let
35, X = 10,
and
P (X > 65) = .18
X
be the mass in grams of a randomly selected widget. Thus
We also let
X
X =
be the average mass of the 100 widgets in our random
X = 35
Mathematics 231 Homework 1 Solution (Problems #1-8 and 10)
(1) SOLUTION TO PROBLEM 1:
(a) Not Justied. Sampling variation needs to be considered.
(b) Not Justied. First the percentage obtained from the proportion 96/7500, is incorrectly calculated.
Sampli
Mathematics 231 Solution to Problems #81-86
(81) SOLUTION TO PROBLEM 81: Our observed value of
p is
21
100
= .21.
Thus, the
100(1 )
% condence
(.21)(.79)
.21.040731z/2 . For 98 % (respectively 95 %) condence,
interval will be given by .21z/2
100
this bec
Part I. Short—Answer Questions. All questions count for 4 points.
Write your answers in the spaces ( ) provided after each question. .
You need not show work and no partial credit will be given. Final answers
must be simpliﬁed.
1. Suppose that X is a rand
Part (I. Short—Answer Questions“ Point-values of questions are as
indicated. spaces ( ) provided after each question. You need not show
'Work and no partial credit will be given, Final answers must be simpliﬁed.
Questions 1, 2 deal with the following freq
Mathematics 231 Solution to Problems #18, 19, 21-24
(18) SOLUTION TO PROBLEM 18:
(a) F. Sampling variation must be taken into account.
(b) T. This is a correct inference from information about the sample proportion (assuming that the sample
is chosen at r
Mathematics 231 Solution to Problems #25-28
(25) SOLUTION TO PROBLEM 25:
k1 = 10 members, the second with
k4 = 6 members, and so the
24!
; a large number!.
10! 5! 7! 6!
(a) The 24 interns are being divided into four groups, the rst with
k2 = 5
k3 = 7
memb
Mathematics 231 Solution to Problems #35-40
X , we see that the possible values of
X are x = 5, x = 0, x = 1, x = 3. Therefore, the events X < 1 and X 0 are, respectively, equivalent to
X = 5 X = 0, and to X = 0 X = 1 X = 3. Therefore, p(X < 4) = p(X = 5)
Mathematics 231 Solution to Problems #29-34
S
(29) SOLUTION TO PROBLEM 29: If we let
and
E
note.
be the event that the randomly chosen person is a smoker,
be the event that the randomly chosen person develops emphysema, then there are two things to
The rs
1
Mathematics 231,
Spring, 2014
Reading and Practice Problems, Part II
Textbook: Statistics for Engineers and Scientists 3rd edition, by William Navidi.
Section
Topic
Practice Problems
Chapter 4. Commonly Used Distributions
4.1
4.2
4.3
4.4
4.5
4.5
4.6
4.7
NIATHENIATICS 231
Test 2, Thursday, November 5, 2015 '
Name: ‘ ' V ‘ (Please print
Please circle your instructor’s name and the time your class meets.
, Prof. Stanley Prof. Bandyopadhyey Prof. Neel
MWF 8:1‘0 MWF 9:10 MWF 2:10
This is a closed book, no
MATHEMATICS 231
Test 1, Thursday, October 1, 2015
Name:
SOLUTION
Part I. Short-Answer Questions. Point-values of questions are as
indicated. spaces (
) provided after each question. You need not show
work and no partial credit will be given. Final answers
MATHEMATICS 231
Test 1, Thursday, Oct 4, 2012
Name:
(Please print.)
Please circle your section number and the time your class meets.
Section 010
MWF 9:10a
Section 011
TR 2:35p
This is a closed book exam. You may use a calculator, however, in Part II, you
Mathematics 231 Final Examination April 30, 2009
PART 1. /70 pts 18. /22 pts
15. /22 pts 19. /22 pts
NAME gg/u 25ml» 16. /20 pts 20. /22 pts
SECTION 17. /22 pts TOTAL /200 pts
This is a closed book exam. You may use the one sheet (both sides) of formulas
Practice Final
Math 231, Spring 2013
Part I
The rst two question are based on the following: For a set of bivariate data (x1 , y1 ), . . . , (x12 , y12 ),
the least squares line is computed to be y = 2 4x. Suppose that the sample mean of x is 1, the
sampl
Practice Final
Math 231, Spring 2013
Part I
The rst two question are based on the following: For a set of bivariate data (x1 , y1 ), . . . , (x12 , y12 ),
the least squares line is computed to be y = 2 4x. Suppose that the sample mean of x is 1, the
sampl
Mathematics 231
Final Examination
PART 1.
15.
April 30, 2009
/70 pts
/22 pts
18.
/22 pts
19.
/22 pts
NAME
16.
/20 pts
20.
SECTION
17.
/22 pts
TOTAL
/22 pts
/200 pts
This is a closed book exam. You may use the one sheet (both sides) of formulas and example
MATHEMATICS 231
Practice Test 2-01 Solution key
2
2
1. Given E(XY ) = xyf (x, y)dxdy = 8, X = 2, Y = 3, X = 4, Y = 1, Cov(X, Y ) =
E(XY ) X Y = 8 2 3 = 2 (this indicates the dependence between X and Y ),
2
2
2
Z = 4X 2Y , Z = 42 X + 2(4)(2)Cov(X, Y ) + (2
MATHEMATICS 231
Test 2, Thursday, April 03, 2014
Name: SOLUTION
(Please print.)
1. Suppose that X, Y are random variables with standard deviations x = 2; y = 3.
Let Z = 3X 2Y, and given that z = 6. Find the value for the covariance between X and Y,
namely
MATHEMATICS 231,
Spring 2014
Practice Test 202
SOLUTION
1. Suppose that X is a random variable, and that all that is known about X is that x = 2,
x = 1. What is the smallest possible value for P (0 < X < 4)?
3
Answer: (4 points) 4
1
3
P(0 < X < 4) = P(0 2
MATHEMATICS 231
Practice Test 2-02
Part I. Short-Answer Questions. Write your answers in the spaces (
) provided after
each question. You need not show work and no partial credit will be given. Final answers must be
simplied.
1. Suppose that X is a random
MATHEMATICS 231
Practice Test 2
The format of the test is similar to the format of our test (6 short answer,
no partial credit questions followed by 3 regular problems where partial
credit is possible and work must be shown), but some of the questions may
Mathematics 231: Probability & Statistics
Assigned Problems
Note: The numbering of exercises refers to the 4th edition of the textbook.
GENERAL DISCLAIMER: All of the statistics given involve completely fictitious,
made-up numbers!
1. A quality control pr
Mathematics 231 Solution to book exercise 1.2.14
bf This is aX
fairly X
interesting
problem which I did not have time to present in class. It illustrates how the summary
2
statistics,
xi ,
xi can be used to advantage, together with the alternate formula f