Download EXAM I REVIEW – Chapters 1 and 2

MTH 265 – Statistics for Scientists and Engineers
EXAM I REVIEW – Chapters 1 and 2
For this exam you may bring ONE 8.5 inch by 11 inch page of notes ONE SIDE ONLY. You may put
any formula on your note page. You may NOT put examples with solutions or any of our homework
problems with solutions on your page. Inappropriate items on your formula sheet will be removed
before you take your exam.
1.1
Sampling – Know the vocabulary
 Be able to define a population given a process of sampling.
 Be able to determine whether a population is tangible or conceptual.
 Be able to explain why simple random samples always differ from the population in some
ways.
 Be able to determine whether a sampling technique could be classified as a simple random
sample.
 What does it mean if items in a sample are independent?
1.2
Summary Statistics
 Be able to determine the difference between a statistic and a parameter.
 Be able calculate a sample mean, sample variation, sample standard deviation by hand.
 Be able to find the median, mode, range and quartiles of a sample.
1.3
Box Plots
 Be able to calculate and use the first quartile, second quartile, third quartile, and inner
quartile range to construct a box plot for a set of data.
 Know how long to draw the “whiskers” for the box plot and know what makes a data value
an outlier…there is a formula.
 Know how a box plot separates the data into four parts and know what percentage of data
falls into each of the four parts.
 If I give you a completed box plot, be able to identify all important aspects of the box plot
and answer questions about it.
2.1
Basic Ideas
 Be able to find the sample space for an experiment. Tree diagrams often help.
 Be able to find the subset defined by a particular event from an experiment.
 Be able to determine whether two events are mutually exclusive.
 Be able to find the union or intersection of two events, and the complement of an event.
 Be able to calculate the probability of an event from an experiment using the concepts of
mutually exclusive events, the union or intersection of two events, and the complement of
an event.
2.2
Counting Methods
 Be able to apply the Fundamental Theorem of Counting.
 Be able to calculate the number of permutations of k objects chosen from n objects.
 Be able to calculate the number of combinations of k objects chosen from n objects.
 Be able to calculate the number of ways n objects can be partitioned into groups of several
sizes.
 Be able to calculate the probability of an event occurring using the counting methods of this
section.
2.3
Independence
 Know what it means for two events to be independent.
 Be able to calculate probabilities for problems involving independent events.
 Be able to calculate the probability a system functions given components in series or
parallel or both.
2.4
Random Variables
 Know what a random variable is.
 Be able to determine whether a random variable is discrete or continuous.
 Be able to find the probability distribution and the cumulative distribution function for a
discrete random variable for a given experiment.
 Be able to find the probability of event occurring for a discrete random variable for a given
experiment.
 Be able to find the mean, variance, and standard deviation for a discrete random variable
from a given experiment.
 Be able to find the probability of event occurring for a continuous random variable given
the probability density function.
 Be able to find the mean, variance, standard deviation, and cumulative distribution function
for a continuous random variable given the probability density function.
 Given a cumulative probability distribution function, be able to use it to find the median or
any percentile.
2.5
Linear Functions of Random Variables
 Be able to find the mean, variance, and standard deviation for a linear function of a random
variable with known mean and standard deviation…see pages 116, 117, and example 2.48.
 Be able to find the mean, variance, and standard deviation for a linear combination of
independent random variables with known means and standard deviations…see pages 118,
119, 120, and example 2.50.
 Be able to find the mean, variance, and standard deviation of a sample mean from a
population with known mean and standard deviation….a VERY important result. See pages
122 and 123. Study example 2.51.
Your exam will be Friday, January 22nd during class. You will have 50 minutes.
Practice the odd-exercises I assigned with each section if you have not already done so. Those would
make very good exam questions and you have access to the solutions. Review the even-numbered
problems that you turned in. Any of those would make good test questions.
Be sure you have read the sections. I will be testing you on ideas and vocabulary as well as math
processes.
Other problems you could try for practice are located in the Supplementary Exercise sets:
Supplementary Exercises for Chapter 1 (p. 43-44) 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Supplementary Exercises for Chapter 2 (p. 158) 1, 2, 5, 6, 7, 8, 12, 14, 17, 23, 28, 29abc
.