Download Date:

Date:
25 Jan 2005, 09:36:09 AM
Subject:
315 Exam coverage
Week 3 slide 24, the first row of the table, the last entry should be 0.8405.
I've posted a .pdf version of Week 2 key on the website (some are unable to
read the .doc version).
FROM MY PREVIOUS MESSAGE:
For week 3 (begins Monday, January 24) you are to read pp. 94-96 lightly but
will not be tested on it.
Read pp 97-136 carefully, especially concentrating on Bayes Formula, tree
diagrams and the OIL example (to be introduced in the in the lecture slides not
yet posted).
Carefully study expected value of random variable, variance and standard
deviation of random variable, properties
E (a X + b Y + c) = a E X + b E Y + c
and
s.d (a X + b) = |a| s.d.(X),
where a b c are constants and X, Y are random variables.
Also, for INDEPENDENT random variables
E (XY) = (E X) (E Y)
and
Var(X + Y) = Var(X) + Var(Y).
FROM MY PREVIOUS MESSAGE:
Our next readings are in Probability. Lectures will not meet Monday.
Carefully read pp 70-93 for Wednesday lecture. I will post the slides tomorrow
(Friday) afternoon and suggest exercises at that time. This is an interesting
part of 315 and my experience is that students gain a solid understanding of
probability from this course.
Your main focus:
1. The set of all possible outcomes and its subsets "the events" as a
model for probability. Union, intersection, complements of events. Venn's
diagram.
2. Addition rule for probabilities, e.g. P(rain today or tomorrow) =
P(rain today) + P(rain tomorrow) - P(rain both days).
3. Multiplication rule for probabilities, e.g. P(rain today and
tomorrow) = P(rain today) times the conditional probability of rain tomorrow
given that it has rained today, written P(rain both days) = P(rain today)
P(rain tomorrow | rain today). The previous expression has in it a vertical
bar (not a division sign) with the event whose probability is sought left of
the bar and the conditioning event right of the bar. So if we think there is a
40% chance of rain today and if we think there is a 3% chance of rain tomorrow
if it does indeed rain today then P(rain both days) = 0.4 times 0.03.
4. Independence of events means having one event occur does not affect
the probability of the other. If P(rain tomorrow) is not affected by whether
it rains today that would be an example (if it were true). In such a case
P(rain tomorrow | rain today) = P(rain tomorrow).
5. We'll use the example of drawing colored balls from a box e.g. if
drawing with replacment from {R R R B B} then P(R1) = 3/5 (red on draw one).
Because we replace balls P(R1 and R2) = P(R1) P(R2 | R1) = (3/5) (3/5). We've
used the fact that if a red is drawn on draw one the conditional probability of
a red on draw two remains 3/5 (we've replaced the red). On the other hand, if
we do not replace balls P(R1 and R2) = (3/5) (2/4) since the second draw is
from 4 balls, only two of which are red if a red was slected first.
FROM MY PREVIOUS MESSAGE:
For the syllabus and other materials pertaining to Statistics 315 go to
www.stt.msu.edu/~rdl
Once there, clicking on STT 315 takes you to the materials.
Clicking on any offering, such as the syllabus, will result in that file being
downloaded. The syllabus is small but the powerpoint slides may run to a
couple of megabytes. If you work over a modem keep this in mind.
For now, look over the syllabus and the slides found on the website. When you
print the slides it is best to print them 6 to each page.
Kindly do not reply to this message but do bring up your questions in class.
STT 315 students should be "gently" reading all of chapter 1 of the textbook,
but pay careful attention to matters concerning the sample and population
standard deviations. I will focus on skills pertaining to the readings but
narrow them (or in some cases enlarge upon them) vis-a-vis the powerpoint
slides found on the website. These matters include:
use of table 14 (random numbers) to conduct random sampling
with-replacement vs without-replacement sampling
why sample at random?
calculation of sample standard deviation s from the definition
calculation of s by "short cut" method (more subject to rounding
errors)
what happens to s if all numbers on a list are multiplied by a
constant?
what happens to s if a constant is added to all numbers on a list?
margin of error: (estimate) +/- (estimated standard error of the
estimate)
special case of above: (sample mean) +/- (s / root(n) ) (n is
sample size)
Great Trick of Statistics
histogram vs density picture of data; the issue of resolution
how to make a density from a list of numbers (do by eye for a few
values)
with replacement is about the same as without if root( (N-n) / (N-1) )
is near 1 NOTE CORRECTION
cloning a population
how many with-replacement samples vs without?
THE FOLLOWING INFORMATION IS NEW.
YOUR PREPARATION FOR EXAM 1, WEDNESDAY FEBRUARY 2:
Look over the slides for Weeks 1, 2, 3, and prepare to solve questions of the
type discussed there.
Likewise, consult the recitation assignments and prepare to solve questions of
like kind.
Consult your textbook as needed per the readings announced in my earlier emails
reported above.
On next Monday I will be able to answer questions concerning any of this
material.
The exam itself will be hand written and you will then select a multiple choice
response to match your answer and record that on a scan sheet. BOTH THE
SCAN
SHEET AND YOUR HAND WRITTEN EXAM PAPER WITH YOUR
SIGNATURE WILL BE REQUIRED.
IF ONE IS NOT SUBMITTED YOU WILL EARN 0.0.
Arrive early enough to assist us with seating. You will be assigned seating
for this exam. ANY STUDENT WHO BEGINS THE EXAM IN A SEAT
OTHER THAN THE ONE
ASSIGNED TO THEM MAY BE ASKED TO LEAVE AND WILL EARN 0.0
AT THE DISCRETION OF
THE INSTRUCTOR.
You can expect 20 questions. Points may be withdrawn for answers given without
justification. You must show enough work to enable us to see that you know
what you are doing. Some students will be audited and their scantron score may
be altered to reflect the work they have shown on the written exam.
If you are prepared as outlined above this exam should pose no unexpected
difficulties.
The textbook exercises are keyed to sections of the book which will also give
you an idea of where the emphasis lies.
R