Course 189-323: Probability Theory: May 2001

McGill University, Department of Mathematics and Statistics
189-323: PROBABILITY THEORY (May 2001)

Frequently Asked Questions (FAQs)

Question / Suggestion Response
May 27 For Q14, I understand the flaw as being that the librarians didn't take into consideration the publication year of the computer science books. Though they are newer, they were still used the same amount of time as the older physics books thus obtaining the same amount of damage. I do not see how this relates to the story involving women physicians. the flaw is that they analyzed the data only from the ones who died

there are not that many older women mds.. women in medicine is a relatively new phenomenon..

If the age profile of the men and women doctors is as follows
(back to back histograms)

...............age ................

which profile is going to generate younger deaths?
  For Q3 part 3: I need a hint or 2. I know the mean amount of cans filled under 355 is np = (6)(0.16)=0.96 cans. Where do I go from there?

Q16: I made a 5x10 table to find the distribution. Is that correct?

Q3 part one is about counts of cans, can't say much about the total amount of soft drink from a count of no. of cans.

and b is about sums or means of amounts

two different distributions .. have we had others with sums of continuous variables?

q16 did you check that the probabilities all add up? do they look reasonable and in line with your intuition?
In sample final examples:

2) For Q4, I used P(S | W) = P(S)P(W | S) etc.
Is that a correct approach?

3)In Q5, what do you mean by "how does it compare"? I calculated the mean cost without paying which is greater than the $25 that it costs if one paid.

4)In Q7a, what does "the count X" mean?

5)In Q8, what distribution does it look like? It seems neg. exponential like, but this is a discrete distribution!

6)In Q9, b,c,d are copied from Q7 and don't belong.
2) you seem to be on right track .. .i.e. working forward from left to right as one does in a tree, then focus on those paths that lead to W etc
ie identify the paths ending in W, and go sort them out as to where they started . I don't memorize these formula any more .. I represent them in the tree..

3) Comparison shopping means calculating which is cheaper, n'est pas?

4) my mistake for switching notation in midstream. I will change all to Y

5)yes it IS discrete.. keep looking ..
if you don't focus on the $0 and $5
and instead change the outcome to 'did not win' and 'did win'
(the fact of winning, not the amount)
what is the sum now?

6) thanks.. will put right .. the downside of cut and paste..
May 27 1) When do we use P(A or B) = P(A) + P (B)
versus P(A or B) = P(A) + P (B) - P(A and B)?

IF P(A and B) is zero, then it can be omitted and you have the simpler 1st version where A and B are mutually exclusive

We have the same 'general vs special' case for multiplication rule..

general rule is P(A then B) = P(A) P(B given A)

BUT if P(B given A) is the same as P(B), then the multiplication rule simplifies to the one where A and B are independent.
  Beisdes that, I would like to know if we went over 7.5 from chapter 7 in class. We used it much earlier.. we approximated the sampling distribution of the proportion (a) of Canadians who favour same-sex marraiges (b) births that are male, (c) no-shows for airline flights, etc..

We noticed that Normal Approximation also worked well for Poisson and Gamma distributions with large means and little of the probability distribution 'down against the Y=0 boundary' .. we emphasized sketching the distribution to see if in fact it fits.. (These are all applications of the CLT, as long as we can see how the r.v. of interest is a sum or mean of n i.i.d. rv's)

So answer is .. yes! Actually we spent more time trying to come up with a rough rule of thumb for when it applies (top 4 lines of p 312 paraphrases our 'if it fits, use it' approach)
I was wondering if it would be possible for you to give us tomorrow an example sheet of equations that you are willing to give us for the final exam. That way, I can maybe study the equations that you are not going to give us. Also, it would help to do the practice problems with only that sheet of equations in hand since that is all we are allowed for the final. I will provide the relevant formulae from appendix 2 of the book

I will expect you to know , and know how to use, the definitions and formulae for

experiments and associated concepts, probabilities of events

additive and multiplicative Laws

conditional and marginal probabilities, independence

law of total probability, Bayes Rule

probability distribution

expected value of a r.v., or function of one or more rv's
in particular, variance of a r.v. and of linear combination of r.v.'s,
covariance of 2 r.v.'s

density function (pdf) and (cumulative) distribution function

joint probanility distribution

distribution of function of one or more rv's

- method of Distribution Functions and Transformations

- sums, averages and proportions, exact and approx. (via CLT)
May 21 Could you paste the solution of Exercises around chaper 4 and 5. I have done it, but I want to check my answer. Thanks! See the web site.. I have been adding them to the web site all weekend.. As of now, I am just missing the last few.. 5.68, 5.94, 5.95

Are these the ones (from the book) you were referring to?

Or do you mean the ones I made up to give and idea of what i would ask on the quiz.. ?

For the latter, I don't have time right now to do solutions for them, and in any case I might use some of them -- directly or indirectly -- on the quiz..

So if you have done them all the better..
  I was wondering whether we must memorize both the normal and the gamma distribution equations. NO. We do not use the normal density that much, more the cdf -- and the cdf doesn't not have a closed form.. hence the tables and Excel and calculator functions.. As for the gamma, I do not remember it off the top of my head .. but I do remember (and would want you to too) that the gamma with an (integer) shape parameter (a) can be represented as a sum of (a) independent r.v.'s, each with an identical exponential distribution. Also the gamma will come up again later this week, with the important chi-square distribution.
May 15 Plus, could you also post the averages of the assignments, i.e., class average so far, quiz, etc on the web, so we could see each of us stands in the course, i.e., comfortable level or panic level. will do...
  The assignments are fine as they are, I'm sure you've noticed people have already worked in 'groups', so in that sense they should also be able to 'figure out' the tougher questions  
  The quiz was perfectly fine as it was. It did involve a few tricks, but they were only in how the question was worded. Even though I didn't get a very high mark, I feel I made silly mistakes that me a 20%; if you keep the exam the same as the quiz, that would be great  
  More concrete examples to give better idea on methods to
problem solving different types of questions.
  I have trouble taking notes on your excel spreadsheets and
graphs. Even when I understand them I am unable to write down something to study from later on which will help me understand it again. More actual examples on the board would be nice also. Your a great teacher.
Maybe trying to have a more organized lecture in order for it to be easier to follow. What I mean by that is that you give us the necessary theory of the chapter and before the end of class, you choose a number from the book to conclude what we have learned  
May 15 I've got a request concerning your 323 probability class. Since it isn't very "note-friendly", it would be great to have more CORRECTED exercises from time to time. Or maybe actually solve some during class. As others might have pointed out, jumping quickly from topic to topic doesn't always give us time to grasp the more detailed and difficult parts of the chapters. The book's solutions are downright pointless since they never show the reasoning we should use to get to the end result, and we're not even guaranteed a correct answer.

It would hugely useful for practicing and knowing how to solve key exercises for the final.

Another question : I went to the 4:30pm tutorial twice, and nobody was there. Not even other students. how do tutorials work? Does someone solve exercises or just answers our questions? Or am I missing something?
May 15 I am in your Probability Theory class. Am I correct in assuming that since there is no assignment posted for tomorrow it has been cancelled? I just want to make sure that the one that is due on Friday according to the website is not in fact due tomorrow. none tomorrow.. friday is correct..
May 15 Dear professor:

I am a student of 189-323 this summer. You are a very good prefessor.

I have some idea about this coures:

There are a lot of chinese students taking this coures. It is very difficult to follow your lecture, You move from one topic to another too quickly. So it is really hard to take this course. Could you write some notes on the blackboard step by step?

Another thing is about the quiz:

Your question is not easy to understand, we must take a lot to read it. This is out of the course. It becomes testing English reading.

For exapmle: you ask "what is the probability that the side facing down is also " tail"?

I can't understand what is meaning of the side facing down? But in my test paper, you ask to count the probability of two tails coins of the "tail" coins? It is very easy to understand.

In the first question of the quiz, I also can't understand the question. Some word such as " flat tire ".

So could you write the final exam in normal English? For example, the text exercise is esay to understand.


your student.
Thanks for taking the time to tell me your concerns..

I will discuss this further tomorrow, and see how others are faring with my style...

Meanwhile I can promise you that for the final exam, wherever a question is based on a considerable amount of text, I will make the text (explaining the context) available ahead of time..

I make no apologies for using "words" to go with the statistics
and probability.. This is after all a course in applied probability,
and it is difficult to "apply" using just x's and y's..
May 15 Hello, I'm wondering whether time or place has changed for tutorials because I went there yesterday (monday) and today, and no one was there. The web page still advertises same time/place. Please let me know. SORRY. I was busy preparing the next assignment and plain forgot!
Were you the only one? I was there at 8.15 today and Mon.
I will be there tomorrow am -- and in the pm if you or others let me know (remind me) you will be there..

Jim H
May 15 I went on the web site and didn't see any exercices given for the assignment we are supposed to due on Wednesday. Maybe it is my version of Explorer & Netscape that cannot read them, but I only see a red X
on the W 16 box.

Is there anything to hand in for tomorrow class?
No.. but i just set one for Friday...
May 10 I was wondering where would be a good place for students to drop-off their
assignments on the given due dates. The math office closes at 5:00 each day,
so I was wondering whether it is convenient if we are able to drop-off assignments there by 5:00 on days that they are due, and that that way, you could just pick them up from your mailbox anytime after then.

May 9 I haven't looked entirely in depth yet, but I was wondering what you meant by "lessons" in the last part: 'What lessons can you draw as to when we could approximate the Poisson distribution by the Gaussian (Normal/Bell shaped) distribution.

Did you mean that we should figure out what to look out for (or significant details to notice) about given factors in a problem that would simplify Poisson distribution into a Gaussian distribution?
yes, that's what I meant.. if you play around with the (ONLY ONE) adjustable parameter of the Poisson distribution, you start to see how it
changes shape.. (a bit like how its cousin, the binomial, does) If you don't have time to play around with many of them, take a look at pp 18-19 of my notes for course 626.
  My question is about how much the assignments, the final and the quizzes count for the final grade evaluation. I know you wrote it in the course outline on the webpage, and maybe it's just me, but I can't seem to understand a thing of what's written. Maximum of (1,2,3), where

1=Final Exam only

2 = 1/4 for Assignments[best k/(k+1)]
+3/4 for Final Exam

3= 15/100 for Quizzes
+25/100 for Assignments[best k/(k+1)]
+60/100 for Final Exam

  Could you please give me the name of the book you were referring to ? Something by Moore and McAbe... Intro to practice of stats HTTP://WWW.WHFREEMAN.COM/STATISTICS/MASTER.HTM
07 May We are a little confused about what value you are asking for in the Breast Cancer data: questionf (the second one). It is part A... did you want the value in days of at least how long the top 5 percent waited, or how many people are in the top 5%, or ...something else? the 50th percentile is the median (1/2 the values are above it, half below it)

the 25th percentile is the data value such that 3/4 are above it and 1/4 below it
the 95th percentile is the data value such that 95% are above it and 5% below it
Percentiles are values of the variable (in this case, they are measured in days)

Definition from Armitage and Berry3, p 34

<<The value below which P% of the values fall is called the P-th percentile >>
04 May Slow down with definitions. I didn't really get the combinations and permutation and mn rule  
.. Real life examples are great. speed of lecture too slow. need to lecture quicker.  
.. Allow people only 3 questions per class so they don't keep disturbing you AND us; plus ask people to lift their hands before asking a question. Agree. Will do.
.. Prof Hanley, Course is made interesting and evaluation method seems fair. It's a pleasure to come to class.  
.. I'm not sure how well your method complements the book. Will you introduce us to the material and allow the textbook to clear up any holes or will you just confuse us? Will your method clash with the book's?

Will we have enough time to cover all the material? It seems we're going pretty slow for such basic material.

Also, please keep tangents to a minimum. Do the non-comp-sci majors care for a 15-min lecture on algorithm generation? This isn't a programming course, so why are we wasting time talking about the history of MS Excel?

I give an A for effort though. Your explanations are well explained and indepth. Yur love and mastery of the material shines through.
02 May I'm a student in your class. For the question in assignmnent 2, I found the loto-quebec page in your website but I couldn't find any form for the super 7 lottery game. sorry.. it is there now

Thanks for telling me...
.. I'm a student in your 323 probability theory summer class, and I have a small question regarding the latest assignment.(Due tomorrow, may 3rd) On the website, inside the assignment box, you have written "2.8,2.9,2.14,2.15 from WMS5". These most probably refer to exercises in the book, but I can't seem to find them...
There are many different "2.8"s in the book, referring to either theorems, exercises, examples or chapters...

Any help would be appreciated.
EXERCISES 2.8,2.9,2.14,2.15 from WMS5 are on pages 29,34

where is theorem 2.15?
.. Can I met you before the course tomorrow, around 8h30 am at the usual classroom, I would like to copy theexercices from the manual.

Most people I talk with didn't get the 5th edition, and there is no more left at the bookstore.

just let me know if you can. Thank you very much
i checked with bookstore who tell me (as of 4.39pm) that "there are > 30 copies left.. they just have to look on other side of shelf.. not the 100 not the 200 but the 300 section.."

mind you, I had trouble finding the shelf myself last week when i went in to check.. at that time there were > 50.. i did tell the bookstore people that maybe they could signpost better...
.. I wanted to clarify the numbers for the assignment. They include 4 numbers from the textbook as well as your homegrown question? yes, as it says on web page...

2.8,2.9,2.14,2.15 from WMS5

Q3 (homegrown) from p2 of here (here being a link to exercises_around_chapter 2, dealing with a loto-quebec lottery)
01 May I am a student in your Probability course and I'd like to know if the 2nd edition of MATHMATICAL STATISTICS

I don't really want to pay 80$ and I found the 2nd eidtion at the library.
This is my 1st time with this course and text, but I doubt if it has changed that much.. math/stat is a fairly static area..
compare with others who have version 5

you will need to look up the exercises in ver 5

also, you cannot rely solely on my notes; they will not be sufficient [I don't believe in duplicating the material in an already best selling book]