MHC 503 Cartesian Coordinates in a Mathematical Graph Questions
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I need help answering the following discussion questions, 2-2, 2-4, 2-6, 2-8, 2-10, 2-14, 2-16, 2-20, 2-24, 2-26, 2-28, 2-32 and the WTVX case study. I will attach pictures of the problems below.
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APPENDIX 2.1: DERIVATION OF BAYES’ THEOREM
79
Case Study
WTVX
WTVX, Channel 6, is located in Eugene, Oregon, home of
the University of Oregon. The station was owned and oper-
ated by George Wilcox, a former Duck (University of Or-
egon football player). Although there were other television
stations in Eugene, WTVX was the only station that had a
weatherperson who was a member of the American Meteoro-
logical Society (AMS). Every night, Joe Hummel would be
introduced as the only weatherperson in Eugene who was a
member of the AMS. This was George’s idea, and he believed
that this gave his station the mark of quality and helped with
market share.
In addition to being a member of the AMS, Joe was the
most popular person on any of the local news programs. Joe
was always trying to find innovative ways to make the weather
interesting, and this was especially difficult during the winter
months, when the weather seemed to remain the same over long
periods of time. Joe’s forecast for next month, for example, was
that there would be a 70% chance of rain every day and that
what happens on one day (rain or shine) was not in any way
dependent on what happened the day before.
One of Joe’s most popular features of the weather re-
port was to invite questions during the actual broadcast.
Questions would be phoned in, and they were answered on
the spot by Joe. Once a 10-year-old boy asked what caused
fog, and Joe did an excellent job of describing some of the
various causes.
Occasionally, Joe would make a mistake. For example, a
high school senior asked Joe what the chances were of getting 15
days of rain in the next month (30 days). Joe made a quick calcu-
lation: (70%) X (15 days/30 days) = (70%)(1/2) = 35%.
Joe quickly found out what it was like being wrong in a univer-
sity town. He had over 50 phone calls from scientists, mathema-
ticians, and other university professors, telling him that he had
made a big mistake in computing the chances of getting 15 days
of rain during the next 30 days. Although Joe didn’t understand
all of the formulas the professors mentioned, he was determined
to find the correct answer and make a correction during a future
broadcast.
Discussion Question
1. What are the chances of getting 15 days of rain during the
next 30 days?
2. What do you think about Joe’s assumptions concerning
the weather for the next 30 days?
Discussion Questions and Problems
Discussion Questions
2-1 What are the two basic laws of probability?
2-2 What is the meaning of mutually exclusive events?
What is meant by collectively exhaustive? Give an
example of each.
2-3 Describe the classical method to determine probabil-
ity with an example.
2-4 Describe the addition law for events that are mutu-
ally exclusive and events that are not.
2-5 Describe what it means for two events to be statisti-
cally dependent.
2-6 Bayes’ theorem is an extension of the original prob-
ability. Explain.
2-7 Describe the characteristics of a Bernoulli process.
How is a Bernoulli process associated with the bino-
mial distribution?
2-8 What is a random variable? What are the various
types of random variables?
2-9 What is the difference between a discrete probability
distribution and a continuous probability distribu-
tion? Give your own example of each.
2-10 What is the expected value, and what does it mea-
sure? How is it computed for a discrete probability
distribution?
2-11 What is the variance, and what does it measure? How
is it computed for a discrete probability distribution?
2-12 Why is a normal distribution converted to a standard
normal distribution?
2-13 A card is drawn from a standard deck of playing
cards. For each of the following pairs of events, in-
dicate if the events are mutually exclusive, and indi-
cate if the events are exhaustive.
(a) Draw a spade and draw a club.
(b) Draw a face card and draw a number card.
(c) Draw an ace and draw a three.
(d) Draw a red card and draw a black card.
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