STAT 400

Professor:
John Millson

Office phone
301-405-5156

Class time:
Tu-Th 11:00-12:15

Class location:
Armory 0126

Office hours:
after class on Thursday

e-mail address:
jjmillson@gmail.com

Web page:
www.math.umd.edu/~jjm

Course text:
Probability and Statistics for Engineering and the Sciences, University of Maryland, Ninth Edition by Jay Devore

TEACHING ASSISTANTS

Ying Li

Office: CSS Atlantic Building 4326

Sections
0211,0221,0231 (end in 1)

Office hours Monday 10:00 - 11:00

email:yli42@math.umd.edu

Haeyun Seo

Office: MTH 3301

Sections
0212,0222,0232 (end in 2)

Office hours Wednesday 1:00 - 2:00

email:hys2500@math.umd.edu

Manyuan Tao

Office MTH 0203

Sections
0213,0223,0233 (end in 3)

Office hours Monday 10:00 to 11:00

email:mtao1@math.umd.edu

HW12


SOME MORE EXTRA PROBLEMS TO BE ASSIGNED AT DIFFERENT TIMES IN THE COURSE (don't work on them until they are assigned)

The Theater Problem

1. Suppose three couples go to a theater and sit in adjoining seats. What is the probability that at least one couple is sitting side-by-side?

.

The Boy-Girl Paradox

2. Suppose a friend of yours is a married woman with two children, not twins. Order them by their age.
(i) Suppose she has one girl, what is the probablity both of her children are girls?
((ii) Suppose the youngest child is a girl, what is the probability both of her children are girls?
To do (i) and (ii), first draw the sample space without any conditions { BB, BG, GB, GG}, then draw the conditional sample spaces (they are different) and read off the answer for P(GG| one child is a girl) (i) and P( GG| the first child is a girl) ( the answers are different)

Now things get tricky.
(iiiSuppose your friend tells you that one of her children is a girl. What is the probability both of her children are girls? Assume boys and girls are equally likely.

Now you have to compute P(GG|your friend tells you that one of her children is a girl). The point of (iii) is that the event (your friend tells you that one of her children is a girl) is different from (given one of the children is a girl) because she could have told you one of the children is a boy. For example P(your friend tells you that one of her children is a girl|BG) = 1/2. To do this problem you have to use Bayes' Theorem so you have P(GG|your friends tells you one of her children is a girl) = (by Bayes' Theorem) [ P(your friend tells you one of her children is a girl|GG)] / [ P(your friend tells you one of her children is a girl|GG)P(GG) + P(your friend tells you one of her children is a girl|BG)P(BG) + P(your friend tells you one of her children is a girl|GB)P(GB) + P(your friend tells you one of her children is a girl|BB)P(BB) ]
For example P(your friend tells you one of her children is a girl|GB)= 1/2 and P(GB)= 1/4 so the third term in the denominator is 1/8. (i),(ii) and (iii) have different answers. > There are some paradoxical features about this problem. See Wikipedia "Boy or Girl Paradox" (though this Wikipedia article is not very clearly written).

The Monty Hall Problem (from ``Let's make a deal" a TV show in the fifties)

3. There are three closed doors. Behind one of them is a car (or something else you want) and behind each of the other two is a goat(or something else you don't want). You pick a door but don't open it. Then the host Monty Hall opens another door with a goat behind it. Monty then asks ``do you want to switch''? Should you switch or stick with your original choice? Compute the probabilities of getting the car using the two different strategies ``stick'' or ``switch''.

The two strategies do not have the same success probability. This led to a big controversy in Parade Magazine in the Washington Post about fifteen years ago. I was amazed that one statistics professor (not from U of Md) wrote `` this is stupid, of course they both have probability 1/2 ''. He was dead wrong, so don't believe everything your professors (me included) tell you.

Extra Problem on the equality of the mean and the median

4. Let X be a continuous random variable. Suppose the graph of the density function f(x) has a point of symmetry x0 (this means that if you reflect the part of the curve to the right of the vertical line through x0 you get the part of the curve to the left of that vertical line).
(i) Prove that the mean and the median are both equal to x0 so in particular they are equal.
(ii) Find an example of a continuous random variable X so that the graph of the density function has no point of symmetry but the mean and the median of X are still equal.

THE COURSE LECTURES

In addition to the text, I want you to download my lectures.

HAND-PRINTED LECTURES

Here is a complete set of scanned hand printed lectures (easy to read) available in pdf format.
Professor Millson's Handwritten Lectures

SLIDES FOR MY COURSE LECTURES

Here are typed slides for my lectures - the slides I used in class.

MIDTERM AND FINAL DATES

The first midterm will be in the lecture hall ARM 0126 on Thursday, October 18 and the second midterm will be in ARM0126 on Thursday , November 15.

The final exam will be in ARM0126 on Wednesday, Dec. 12 from 8:00 to 10:00 AM.

The homework quizzes, exams and final will be conducted according to the following rules.
1. No notes and NO "CHEAT SHEET".
2. No text.
3. No laptops
4. No calculators
5. No cellphones.

I will provide you on the exam with the formulas/tables you will need.

HOMEWORK ARCHIVE

All previous homework assignments are archived here HW archive

-->

COURSE DESCRIPTION

We will cover the following topics in the order given..
1. All of Chapter 2.
2. All of Chapter 3
3. All of Chapter 4 except for the last two sections.
4. All of Chapter 5 but very little multiple integrals.
5. Random Samples (from handout) .
6. Some of Chapter 6 on point estimation.
7. Random intervals (from handout).
8. Some of Chapter 7 on interval estimations.
9. Moment generating functions (from handout).

COURSE GRADE

Your course grade will be determined from the following:

Test #1 50 points
Test #2 50 points
Homework 50 points
Final exam 100 points

Total 250 points

If you get 125 points or more you will get at worst a C-. If you get less than 125 points you
will get an F.

Your homework grade.
The week's homework will be assigned on my web page after the Thursday class

THE HOMEWORK QUIZZES

For the first 35 minutes of your TA section on Monday your TA will do the HW problems (if you are lucky he/she will do the one you are about to be tested on). At the end (fifteen minutes left) of your TA section your TA will pick one of the HW problems, you will put away your notes, do the problem and hand it in. In other words every week you will have a HW quiz. On occasion you may be asked to hand in an entire assignment or a part of one.
If you have an excused absence from a HW quiz (TA session) you have two choices:
1. Do the entire assigment and hand it in before the TA section in question (your TA will then grade the relevant question).
2. Otherwise you will receive the grade of E (excused) for the week's HW quiz and your homework total will be rescaled by the appropriate factor (larger than one).

All HW quizzes will count (I will not discount your two worst quizzes as is sometimes done).

MAKEUPS

There will be no makeup for the final exam or midterms except in case of medical emergency, family medical emergency, job interview or university related absence. If you have a medical emergency we will need a note verifying that from a medical professional. If you have a job interview we will need to see written evidence of that interview and interview date. In particular there will be no makeups for family vacations so be careful about buying airplane tickets.

If you do miss a midterm or the final without being excused notify me that you have missed the midterm or the final within a week. Otherwise you will receive a zero.

GRADING APPEALS

After each midterm or HW quiz students have one week from when the midterm or quiz is returned to appeal the grading. No appeals for regrading work done during the semester (including the midterms) can be made after the day of the final exam. Appeals for the final exam must be done in writing.

BACKGROUND EXTRA COURSE NOTES (to be downloaded by you)

  • The pdf file for the solutions of the practice final exam is available right here: PracticeFinalSolutions
    • THE END