4
T
EACHING
S
UGGESTIONS
Teaching Suggestion 2.1:
Concept of Probabilities Ranging
From 0 to 1.
People often misuse probabilities by such statements as, “I’m
110% sure we’re going to win the big game.” The two basic rules
of probability should be stressed.
Teaching Suggestion 2.2:
Where Do Probabilities Come From?
Students need to understand where probabilities come from.
Sometimes they are subjective and based on personal experiences.
Other times they are objectively based on logical observations
such as the roll of a die. Often, probabilities are derived from his
torical data—
if
we can assume the future will be about the same as
the past.
Teaching Suggestion 2.3:
Confusion Over Mutually Exclusive
and Collectively Exhaustive Events.
This concept is often foggy to even the best of students—even if
they just completed a course in statistics. Use practical examples
and drills to force the point home. The table at the end of Example
3 is especially useful.
Teaching Suggestion 2.4:
Addition of Events That Are Not
Mutually Exclusive.
The formula for adding events that are not mutually exclusive is
P
(
A
or
B
)
P
(
A
)
P
(
B
)
P
(
A
and
B
). Students must understand
why we subtract
P
(
A
and
B
). Explain that the intersect has been
counted twice.
Teaching Suggestion 2.5:
Statistical Dependence with
Visual Examples.
Figure 2.3 indicates that an urn contains 10 balls. This example
works well to explain conditional probability of dependent events.
An even better idea is to bring 10 golf balls to class. Six should be
white and 4 orange (yellow). Mark a big letter or number on each
to correspond to Figure 2.3 and draw the balls from a clear bowl to
make the point. You can also use the props to stress how random
sampling expects previous draws to be replaced.
Teaching Suggestion 2.6:
Concept of Random Variables.
Students often have problems understanding the concept of ran
dom variables. Instructors need to take this abstract idea and pro
vide several examples to drive home the point. Table 2.2 has some
useful examples of both discrete and continuous random variables.
Teaching Suggestion 2.7:
Expected Value of a
Probability Distribution.
A probability distribution is often described by its mean and
variance. These important terms should be discussed with such
practical examples as heights or weights of students. But students
need to be reminded that even if most of the men in class (or the
United States) have heights between 5 feet 6 inches and 6 feet 2
inches, there is still some small probability of outliers.
Teaching Suggestion 2.8:
BellShaped Curve.
Stress how important the normal distribution is to a large number
of processes in our lives (for example, filling boxes of cereal with
32 ounces of cornflakes). Each normal distribution depends on the
mean and standard deviation. Discuss Figures 2.8 and 2.9 to show
how these relate to the shape and position of a normal distribution.
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 Spring '11
 MichaelHanna
 Normal Distribution, Probability, Probability theory, Abu Ilan

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