MA 385 - Introduction to
Probability - Fall 2003
Homework Assignments and
Important Dates
Date and Time of Last Update to This
Page:
09/27/10 03:06 PM
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Important
Dates:
Bonus Homework Problem: Show
that the expected value of the sample variance is the variance of the
distribution from which you are sampling.
Click here for a pdf file with
a more formal statement of this problem. Due on Tuesday, Dec. 2 by
noon.
Quiz 10 (The Last One!): Take
Home Homework Assignment: Section 6.2 Problem 8, Section 6.3
Problem 4, Section, and Section 6.4 Problem 4. Due on Tuesday,
December 2 by noon.
Quiz 9: Take Home Homework
Assignment: Section 5.1, Problems 5.1-5 and 5.1-11. On
problem 5.1-11 also find P(X<=2Y). Due beginning of class on
Monday, Nov. 17.
Quiz 8: In class quiz covers
sections 4.1, 4.2, and 4.4, Monday, November 10, beginning of class.
Note: Changed to take-home, due beginning of class on Wed. Nov.
12.
Quiz 7: Take Home Homework
Assignment: Section 4.4 Problems 10 (Hint: In addition to the hint
given in the book, see the proof of Theorem 4.4-1) and 20. Due
Monday, November 10 beginning of class. Note new due date!
Quiz 6: Take Home Homework
Assignment: Section 4.2 Problems 1 and 5. Due Wednesday,
November, beginning of class. Note new due date!
Test 1:
Wednesday, October 1, Covers Sections 1.1, 1.2, and
Chapter 2.
Test 2:
Wednesday, November 19. It will cover Sections
3.1-3.5, 4.1, 4.2, 4.4, and 5.1.
Final
Exam: Friday, December 12, 2003, 3:00 - 5:30 p.m.
The Final Exam will be comprehensive. Sections covered will
include: 1.1, 1.2, Chapter 2, Chapter 3, 4.1, 4.2, 4.4, 5.1,
6.1-6.4, 7.1, 7.2
In class I will be
handing out a sheet of Probability Drill Problems
from which I will also assign homework problems. Please see me if you do
not get a copy of these problems. I will also ask you to play with some of
the applets in the Virtual
Laboratories in Probability and Statistics. Please see me if you do
not get a copy of these problems. Once I have finished covering a section
in class you will be responsible for the homework problems assigned from that
section. If it takes more than two class periods to cover a particular
section then you should start working on the homework from that section after
the first lecture on that section.
Assignments
| Section of Textbook |
Homework Assignments
with Notes |
| Section 1.1:
Basic Concepts |
Section
1.1 Problems: 1-9 odd. On problem 9 create
the theoretical distribution of X (the number of heads in the two
tosses) like we did in class. Then actually toss two coins and
get an empirical distribution (Note: 50 tosses instead of 100
should suffice). You could also try problem number 9 using the
Virtual Labs Binomial Coin Experiment Applet. |
| Section 1.2:
The Mean, Variance, and Standard Deviation |
Section 1.2
Problems: 1 a,c,d
(plot your mean and an interval that is +- one standard deviation from the mean
on the histograms you generated in Section 1.1), 3, 5
(a little tricky so use the hint!), 6, (since this
is a small data set try using your graphing calculator - answers: sample
mean = 4/3 and sample variance = 264/207), 7
(you
may want to use Minitab and/or Excell and the CD in the back of your book to work
this problem).
Check out the Cool Prob/Stats link page for sites that show you how to use your
graphing calculator to compute descriptive statistics |
| Section 2.1:
Properties of Probability |
Section 1.2
Problems:
1,
3, 5, 6, 7, 8, 9(a), 10, 11, 13, 15, 17.
Probability
Drill Problems: 2.6-2.12
Check out the Virtual Labs Venn Diagram
Applet! |
| Section 2.2:
Methods of Enumeration |
Section 2.2 Problems:
1, 2, 3, 5, 7, 9, 10, 11, 12, 13, 14, 15, 17, 20.
Combinatorial
form for the answers
for the poker hands in problem 15: The notation (x,y) will stand for the combination
"x choose y". Four of a
kind: (13,1)(4,4)(48,1)/(52,5); Full
House: (13,1)(4,3)(12,1)(4,2)/(52,5); Three of a
Kind: (13,1)(4,3)(12,2)(4,1)(4,1)/(52,5); Two Pairs:
(13,2)(4,2)(4,2)(44,1)/(52,5); One Pair - hmmmm......see if YOU can do it! Now for
the fun of it, see if you can determine the probability of a straight, a
straight flush and a royal flush!
Probability
Drill Problems:
2.13-2.24 |
| Section 2.3:
Conditional Probability |
Section 2.3 Problems: 1-11 odd, 15, 17,
18 (Note: The answer to #9 is
1/5)
Probability Drill Problems:
2.25-2.43
(Note: Some of these problems involve the concept of independence
which will be covered in Section 2.4) |
| Section 2.4:
Independent Events |
Section 2.4 Problems:
1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 15, 16, 17
Probability Drill Problems:
Finish problems 2.25-2.43 |
| Section 2.5:
Bayes' Theorem |
Section 2.5 Problems: 1-7
Probability Drill Problems: 2.44-
2.48 |
| Section 3.1:
Random Variables of the Discrete Type |
Section 3.1 Problems: 1-11 odd
Check out the
Virtual Labs Ball and Urn Experiment to see
graphs of the Hypergeometric Distribution for various values of the
parameters. |
| Section 3.2:
Mathematical Expectation |
Section 3.2 Problems: 1, 3, 5,
7, 8, 9, 11, 13, 14, 15, 17, 18, 19, 21, 23
(Note: See Appendix A for the answer to number 23). |
| Section 3.3:
Bernoulli Trials and the Binomial Distribution |
Section 3.3 Problems: 1 - 17 odd,
18
Check out the
Virtual Labs Binomial Coin Experiment to see
graphs of the Binomial Distribution for various values of the parameters. |
| Section 3.4:
The Moment-Generating Function |
Section 3.4 Problems: 1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 15, 17, 18,
21 |
| Section 3.5:
The Poisson Distribution |
Section 3.5 Problems: 1, 2, 3, 4,
5, 7, 9, 10, 11, 13, 17 (Note: Use the
disk provided with your book and an appropriate software program (Minitab,
Excel, etc.) for the computations in problems 11, 13, and 17.)
Check out the
Virtual Labs Poisson Experiment to see graphs
of the Poisson Distribution for various values of the parameters. |
| Section 4.1:
Continuous Distributions |
Section 4.1 Problems:
1 - 9 odd, 10, 11 - 17, 19
Hand In as Quiz (see above): 12, 14 |
| Section 4.2:
The Uniform and Exponential Distributions |
Section 4.2 Problems: 1 - 5, 9,
10, 11, 13, 19
Hand In as Quiz (see above): 1, 5 |
| Section 4.4:
The Normal Distribution |
Section 4.4 Problems: 1 - 9 odd, 13
(use technology),
17
Hand In as Quiz (see above): 10,
20 |
| Section 4.3:
The Gamma and Chi-Square Distributions. |
Section 4.3 Problems: 1, 4, 5 |
| Section 5.1:
Distributions of Two Random Variables |
Section 5.1 Problems: 1 - 11 odd
(Note problems 5 and 11 are hand-in problems for Quiz 9 (also see the extra
work for problem 11 above)). |
| Section 6.1:
Independent Random Variables
|
Section 6.1 Problems: 1, 5, 9, 14 |
| Section 6.2:
Distributions of Sums of Random Variables |
Section 6.2 Problems: 1 (Determine
mean and variance only, you do not need to find the p.m.f. (but you are
welcome to do so if you want :-)), 5, 7, 8, 9.
Please note your hand-in assignment above! |
| Section 6.3:
Random Functions Associated with Normal
Distributions |
Section 6.3 Problems:
1, 3, 4, 7(a), 9(a,b) |
| Section 6.4:
The Central Limit Theorem |
Section 6.4 Problems:
1, 3, 4, 7, 9 |
| Section 7.2:
Confidence Intervals for Means |
Section 7.2 Problems: 1 - 15 odd |
| Section 7.5:
Confidence Intervals for Proportions |
Section 7.5 Problems:
1 (a,b), 3 - 11 odd |
| Section 7.6:
Sample Size |
Section 7.6 Problems: 7, 9, 11, 14 |
|