*1 The instructor must write out the lecture preps, that
(s)he is already making, in a special TABLE FORMAT.
This TABLE FORMAT is discussed in detail below

The instructor must write out his/her lecture preps electronically

Acclimating oneself to writing in this format isn-t difficult
The TABLE FORMAT is flexible and allows up to 6 table features

*2 The instructor then uses a perl script or visual basic script
to convert the electronic TABLE FORMATS to color coded slides*10

*10 Since the perl or visual basic script executes instantly and
since usage of the TABLE FORMAT requires no extra time
requirements on the instructor it is immediately seen that
the above setup enables conversion of the lecture preps to
a collection of HTML slides.

*1 The URL is http://www.Towson.edu/~rhendel/m231-f02.htm

This URL contains complete information on the course
including the name of the text, syllabus, and linked slides.

However, this presentation is self contained and
understandable without reference to this site.

*1 COMPONENTS correspond to exam units

*2 TOPICS correspond to chapters

*3 Subtopics correspond to chapter subsections

*4 That is: BINOMIAL, NORMAL are TOPICS belonging to the
DISTRIBUTION component. In most texts there are separate
chapters to the BINOMIAL AND NORMAL distributions.

*5 The BINOMIAL TOPIC (Chapter) has SUBTOPICS of
- Expectation
- Variance
- Word problems etc
Each of these subtopics corresponds to a subsection

*1 - The numbered slides are hyperlinked to actual slides.
- Each slide corresponds to 1 html page
- Each slide performs one of the 8 slide FUNCTIONS
developed in the remainder of this paper

The above is the main web design. Various other links are
added as needed and desired. For example
- a COURSE-INFO page or
- a PROBLEMS-DONE page listing problems reviewed in class

*1 http://www.towson.edu/~rhendel/math231-f02/slide44.htm

*2 The slide makes the point that in the situation of the
   first row--average temperature of 70 with little
   variation--you would only eg need to buy one set of clothes
   while in the situation of the 2nd row---average temperatures
   of 50 in winter and 90 in summer-- you would need to
   purchase two sets of clothes. This distinction hilights
   the need for a measure of DISPERSION besides the
   traditional AVERAGE measure

*3 2 further slide components allowing
   explanatory footnotes (or longer footnotes)
   are not illustrated in the slide below as these
   features arent traditionally used in every slide

*10 Again: A fundamental assumption of this presentation
    is that an instructor could acclimate him/her-self to
    preparing this slide electronically  on say notepad
    in about the same time that they could prepare such
    a slide on pencil and paper.

*1 STUDENT QUESTION (CORRECTED 10-29-02)
MORE THAN h is the same, for BINOMIAL, as AT LEAST h+1
MORE THAN h is the same, for NORMAL, as AT LEAST h
h or LESS is the same as AT MOST h for BINOMIAL or NORMAL

*2 STUDENT QUESTION (CORRECTED 10-29-02)
LESS THAN h is the same, for BINOMIAL, as AT MOST h-1
LESS THAN h is the same, for NORMAL, as AT MOST h
h or more is the same as AT LEAST h for BINOMIAL or NORMAL

*3 In the BINOMIAL word problems we use h-1 and a-1
The minus 1 is not present in the normal problems
Also in the normal problems it does not make a big
difference if you use the LESS THAN vs LESS THAN OR EQUAL*10

*4 This is called the CONTINUITY correction. It takes a long
time till students get this correct. I am therefore not
covering it on tests since students expressed a desire
for further practice on the other items

*10 STUDENT QUESTION
----------------
Recall the BINOMIAL RV is DISCRETE (Possible values:0,1,2,..
By contrast the NORMAL RV is CONTINUOUS( eg height=6.1111)

In a discrete rv,eg MORE THAN 10 means 11 or more(AT MOST 11)
In a continuous rv, MORE THAN 10 means 10 OR MORE

The point is that the probability of EXACTLY being 10 feet
tall is 0 (eg you might be 10.001 or 9.999) So we
- dont have to add the minus 1
- dont have to worry about less than or equals

Nevertheless purists can use or omit the equality sign

*11 STUDENT QUESTION
----------------
This table is not in the book. But it is not something
to MEMORIZE rather it is something to UNDERSTAND. All
the slides are logical. For example to analyze

-- MORE THAN 11 --

we ask if 10 is an example of more than 11 (NO)
we ask if 11 is an example of more than 11 (NO)
we ask if 12 is an example of more than 11 (YES)
we ask if 13 is an example of more than 11 (YES)
we ask if 11.0001 is an example of more than 11 (YES)

It emerges that MORE THAN 11 is equivalant to AT LEAST 11

*1 This slide uses HAT data from class. The data was as follows
- There were 14 students in class(4 wore hats,10 did not)
- There were 7 males and 7 females
- 3 students were MALE and had HATS

*1 We will discuss thoroughly CONDITIONING in the next slide

*1 This simple example exposes students to 4 concepts
- The EXPERIMENT
- The POSSIBLE OUTCOMES
- The SPACE (of all possible outcomes)
- The EVENT
The probability measure can then be illustrated using
these 4 basic introductory concepts

*1 There is alot of confusion here
Math textbooks tend to identify the above two descriptions
- EVEN
- {2,4,6}
Actually they are distinct.
- EVEN is the UNDERLYING ATTRIBUTE of the outcomes
- {2,4,6} is the set   of events in the space ASSOCIATED
with this attribute

To form this set simply go thru all points in the space
and see which ones are even.

*2 The probability is usually based on COUNTING

*1 The following notation is used
Q1=25th percentile
Q2=50th percentile
Q3=75th percentile

*2 So L_p is the LOCATION of the p-th percentile
But the p-th percentile is the VALUE in the L_pth row

*3 Either of these answers is correct
- the 4.5 th item on the list 70,80,80,85,90 is the 4th item:85
- the 4.5 th item on the list 70,80,80,85,90 is the 5th item:90
- the 4.5 th item on the list 70,80,80,85,90 is
the average of the 4th and 5th item: (85+90)/2=87.5

This last method is call LINEAR INTERPOLATION(You are NOT
responsible for it)

Excel uses a totally different formulae (and gets different
answers) to compute the pth percentile. Since there is so much
disagreement any of the above answers is ok

*1 It is debatable whether the FORMULA or SPREADSHEET approach
is superior. One can hide the SPREADSHEET by simply
presenting the formula and then going over the
sub-computations in the formula.

*1 Average = Sum of C1 over # Items in C1 = 140/5=28

*2 c3=c1-c2. So 38-28=10. 26-28=-2.

*3 c4=c3^2. eg 10^2=100. Note how the definition of c4 is
different for the SD vs the MD

*4 c5 = Average (C4) = Sum(C4)/# Items= 534/5=106.8
c5 is called the POPULATION VARIANCE
It is denoted by the Greek letter sigma^2

*5 c6 = Sqrt(c5). Sqrt(106.8)=10.33
c6 is called the POPULATION SD (Standard deviation)
It is denoted by the Greek sigma

*1 The emphasis here is on comparing several similar
COMPLEX problems. Thus in this example we compare
the POPULATION SD, the SAMPLE SD etc Each of these
concepts are COURSE CONCEPTS IN THEIR OWN RIGHT.
Hence the purpose of the OVERVIEW slide is to
compare course items that have a great deal of
similarlity

*1 n=# Of data items (Thoughout the course)

*1 This slide summarizes 8 problems on sample means done in
class. The slide is a bit terse for someone not in class
and needs further clarification for full understanding.
These further details are provided in footnotes 2,3.

*2 The 6th column entitled NORMAL? presents 3 possible justifications
for using the Normal distribution(vs the t distribution)
on the sample means

- #1: The problem explicitly states that the POPULATION is NORMAL
and the POPULATION SD is known

- #2: The sample size n >=30 (The point being that a t distribution
with n>=30 can be approximated by the normal distribution)

- #3: The population standard deviation is given AND
  It is reasonable to ASSUME that the population is normally
distributed

*3 The 3rd column entitled WHY SAMPLE MEAN-WHAT KEYWORDS?,
presents the phrase in the problem question that would
enable the student to recognize that the problem is dealing
with SAMPLE MEANS.

This column was included in response to student inquiries:
(How does a student know that the problem is a Sample
mean problem vs a population mean problem).

Such phrases as
- WHAT PERCENT OF THE SAMPLE MEANS ARE...
- FOR A RANDOM SAMPLE...WHAT IS THE PROBABILITY OF THE MEAN....
indicate that the problem is a SAMPLE MEAN (vs
a POPULATION MEAN) problem. Note how several of these phrases
more clearly indicate that it is a SAMPLE MEAN problem.

*1 http://www.Towson.Edu/math231-f02/slide66.htm
http://www.Towson.Edu/math231-f02/slide67.htm
http://www.Towson.Edu/math231-f02/slide68.htm
http://www.Towson.Edu/math231-f02/slide69.htm

*1 This is a LIST CONTRAST slide (It lists all 4 counting functions
relevant to COUNTING problems and contrasts their notations and
names)

*2 This is a LIST-CONTRAST SLIDE (It lists the 4 counting functions
and contrasts their algorithmic rules)

*3 This is a DICTIONARY SLIDE (It shows the CORRESPONDENCE between
WORD PROBLEMS (eg # sets, # sequences) and COUNTING FUNCTIONS

*4 This is a DISTINCTION SLIDE (It distinguishes between SETS,
SEQUENCES and CODES)

*1 Answer to student question: The BIGGER number is always
on the left (5_P_3 is correct; 3_P_5 will not be used
in this course)

*1 The book uses the rule n_P_r= n!/r!. However
the rule I give is simpler computationally
-------------------------------------------------------
-- Multiply downward starting at n(left  side number)
-- have r items in produce (r is right side number)
-------------------------------------------------------

See *10 for an extended example SEE PROBLEMS-DONE
page for a list of book examples done

*2 The book uses the rule n_C_r = n! / (r! (n-r)!)
However the rule I give is simpler computationally
------------------------------------------------------
-- multiply downward starting at n(Left side number)
-- let the denominators go upward starting at 1
-- stop when the denominator = r (Right side number)
------------------------------------------------------

*10 So 7_P_3 is computed as follows
- Start at 7 the left  hand # in 7_P_3
- Use 3 multiplicands (3 is the right hand #)

EXAMPLE: 7_P_3

7      x      6       x      5     = 210
1st #         2nd #          3rd #

In answer to student questions:
--------------------------------------------
If you understand the above description
then forget the abstract notation and
simply learn the rule...To show work you
can suffice with showing numerical work
--------------------------------------------


*11
EXAMPLE: 7_C_3
- Start numerator at 7 (Left hand #) on top
- Start denominator at 1
- Go upwards to 3 (Right hand #)

7           6              5
--   x      --      x      --  = 35
1           2              3

1st #       2nd #          3rd #

*1 Many examples were done in class. Please see the PROBLEMS-DONE
page

*1
One student suggested that if problems are worked out in
say mathematica and the appropriate exe files are on the
system then a hyperlink to a worked out problem in mathematica
would automatically open.

This would solve the problem of presenting worked out problems.
The description of theory and contrasts could probably
still be accomplished in English. Hence future versions
of this approach will focus on techniques relevant to upper
level courses.