Producing models using probability theory and simulation
By Godfried Lawson
Other Materials used:
Textbook: Elementary Statistics
A Step by Step Approach
Second edition
Author: Allan G. Bluman
Internet Resources: www.bbn.org/us.ap_statistics_outline_folder/course_outline.html
www.maths.uq.au/~gks/class/aa0.html
CHAPTER FOUR:
Day 1
Section
4.1 Randomness:
Parameter
Statistic
Population mean, sampling mean The population average ( mu ), the average
of the observations in the
sample ( x-bar )
Randomness and probability
Sampling variability. Different sample mean may produce different
mean value
Independent trials
Activity: Toss of a coin
Homework: Page 218-214 Ex 4.1-4.13
Day 2
Random numbers
Generating random integers on the TI-83.
click here for the
activity folder
Quiz #1 will cover section 4.1
Homework: Page 218-214 Ex 4.14-4.25
Day 3
Section 4.2 Probability Models
A probability model for a random phenomenon consists of sample S and a
assignment of
probabilities P.
Sample space: The sample space S of a random phenomenon is the set of all
possible outcomes.
Event
Probability model
Probability rule: addition rule for disjoint event ( mutually exclusive
)
Homework: page 221-231 Ex. 4.14-4.25
Day 4
Probabilities in a finite sample space.
Assign a probability to each individual outcome. These probabilities must
be numbers
between 0 and 1 and must have sum 1. the probability of any event is the
sum of the
probabilities of the outcomes making up the event.
Intervals of outcomes: p ( 0.3 < x < 0.5 ) ...
Properties of the normal distribution: The normal distribution is
a continuous , symmetric,
bell-shaped distribution of a variable.
1. Bell-shaped curve
2. The mean , median, mode are equal
3. The distribution curve is unimodal
4. The curve is symmetrical about the mean
5. The curve is continuous.
6. The curve never touch the x-axis
7. The total area under the normal distribution curve is equal to
1
8. The area under the normal curve that lies within one standard
deviation of the mean is
approximately 0.68; within two standard deviations , about 0.95 and within
three standard deviations,
about 0.997
Using tables of the normal distribution.
Draw the picture, shade the area decided, look up the z value in the table
to get the area.
Homework: page 232-236 Ex. 4.26-4.37
Day 4
Random variables: Random variable is a variable whose value is a numerical
outcome of a
random phenomenon.
Probability distribution: Probability distribution of a random variable
X tells us what values X can take and how
to assign probabilities to those values.
Day 5
Mid-chapter test review
Homework: Study guide worksheet.
Day 6
Mid-chapter test
Day 7
Section 4.3 Sampling Distributions
Statistical estimation and the law of large numbers
Draw observations at random from any population with finite mean: As the
number of observations drawn
increases, the mean of the observed values gets closer and
closer to the mean of the population.
Simulation of sample distributions: A method or procedure for exploring
and understanding the behavior of
complex processes by doing repeated experiments that resemble the actual
situation.
Simulation of probability distributions
Construction of sample distribution :TI-83 calculator activity: In this
activity, the learner will explore
sampling distribution through simulations of rolling dice. Click
here for the activity folder
Day 8
Mean and standard deviation of a sample mean
Unbiased estimator: Because the mean of the sample is equal to the mean
of the population
Homework: page 248-250 Ex. 4.38- 4.42
Central Limit Theorem.
Sampling distribution of a sample mean
Population N( mu, sigma),... sample N(mu, sigma/square root of n)
Homework: page 221-231 Ex. 4.43-4.55
Day 9 Chapter Review Page 253
Day 10 Chapter test
Why I used additional textbook
I used the textbook :Elementary Statistics as additional material for
this project because the book presents a clear understanding of the multiplication
rules and makes shows the difference between the permutation and the combination.
The book also shows how the tree diagram is a devise used to list all
possibilities of a sequence of events in a systematic way. It is also used
to assign probabilities to each branch and with the multiplication rule,
find the probability of each branch.
The positive aspect of the instructional unit
This group project has helped me in many ways:
* I made an extra effort to read materials we did not learn
in the classroom..
* I designed my own lesson plan which includes the lecture, the
activities to reinforce the theory learned, the assessment
materials to check the level of mastery and I even
use other material which I found very useful to promote a quick
understanding of the topic.
* Over all this project has forced me to recall in a very short
period of time the topics I learned in my statistics class. Also I
feel more confident to teach this course.
