CHAPTER 1
The Nature of Probability
and Statistics
1
The Nature of
Probability and Statistics
CHAPTER 1
OUTLINE
1-1
1-2
1-3
1-4
Descriptive and Inferential Statistics
Variables and Types of Data
Data Collection and Sampling Techniques
Experimental Design
STAT 2013-002
Name: _
CWID: _
The data obtained in a study on the number of absences and the final grades of seven
randomly selected students from a statistics class are given below. Compute the value of the
linear correlation coefficient for the data and
Homework Problem 1.7
A randomly selected car battery is tested and the time of failure is recorded. Give an
appropriate sample space for this experiment.
(Lee J. Bain and Max Engelhardt, Introduction to Probability and Mathematical
Statistics.)
Solutions:
CHAPTER 2
Frequency Distributions
and Graphs
1
Frequency Distributions and
Graphs
OUTLINE
2-1 Organizing Data
2-2 Histograms, Frequency Polygons, and Ogives
2-3 Other Types of Graphs
2
Learning Objectives
1
2
3
4
Organize data using a frequency distributi
Final Review
Chapter 6:2 value, properties of normal distribution and standard normal table (2 table),
central limit theorem, calculate probability (x value) by using 2 table
Chapter 7: Properties of student t distribution and student t table, confidence
Homework Problem 1.27
A bag contains five blue balls and three red balls. A boy draws a ball, and then draws
another without replacement. Compute the following probabilities:
(a) P ( 2 blue balls ) .
(b) P (1 blue and 1 red ) .
(c) P ( at least 1 blue ) .
Homework Problem 1.37
Let P ( A ) = 0.4 and P ( A B ) = 0.6 .
(a) For what value of P ( B ) are A and B mutually exclusive?
(b) For what value of P ( B ) are A and B independent?
(Lee J. Bain and Max Engelhardt, Introduction to Probability and Mathematica
Homework Problem 1.19
Let P ( A) = P ( B ) = 1/ 3 and P ( A B ) = 1/10 . Find the following:
(a) P ( B ) .
(b) P ( A B ) .
(c) P ( B A ) .
(d) P ( A B ) .
(Lee J. Bain and Max Engelhardt, Introduction to Probability and Mathematical
Statistics.)
Solutions
Homework Problem 1.15
Two part-time teachers are hired by the mathematics department and each is assigned at
random to teach a single course, in trigonometry, algebra, or calculus. List the outcomes
in the sample space and find the probability that they w
In this experiment, we randomly chose 51 high school disability students. We want to analysis
two things. The first one is that if the ACT composite / math score is significantly different
between disability types. Secondly, we want to see whether number
Homework Problem 1.33
One card is selected from a deck of 52 cards and placed in a second deck. A card then is
selected from the second deck.
(a) What is the probability the second card is an ace?
(b) If the first card is placed into a deck of 54 cards co
Homework Problem 1.35
In a bolt Factory, machines 1, 2, and 3 respectively produce 20%, 30%, and 50% of the
total output. Of their respective outputs, 5%, 3%, and 2% are defective. A bolt is
selected at random.
(a) What is the probability that it is defec
STAT 5023 HW 5 Cassandra Griffith & Sean Ye
Code:
data air;
input city1 $ city2 $ pass miles inm ins popm pops airl;
l_pass=log(pass);
l_miles=log(miles);
l_inm=log(inm);
l_ins=log(ins);
l_popm=log(popm);
l_pops=log(pops);
l_airl=log(airl);
datalines;
pro
Homework Problem 4.3
Five cards are drawn without replacement from a regular deck of 52 cards. Let X
represent the number of aces, Y the number of kings, and Z the number of queens
obtained. Give the probability of each of the following events:
(a) A = [
Homework Problem 5.1
Let X 1 , X 2 , X 3 , and X 4 be independent random variables, each having the same
distribution with mean 5 and standard deviation 3, and let
Y = X1 + 2 X 2 + X 3 X 4 .
(a) Find E (Y ) .
(b) Find Var (Y ) .
(Lee J. Bain and Max Engel
Homework Problem 6.1
Let X be a random variable with pdf
4 x3 , 0 < x < 1
fX ( x) =
.
otherwise
0,
Use the cumulative (CDF) technique to determine the pdf of each of the following
random variables:
(a) Y = X 4 .
(b) W = e X .
(c) Z = ln X .
(d) U = ( X 0
Homework Problem 6.7
Let U ~ UNIF ( 0,1) . Find transformations y = G1 ( u ) and w = G2 ( u ) such that
(a) Y = G1 (U ) ~ EXP (1) .
(b) W = G2 (U ) ~ BIN ( 3,1/ 2 ) .
(Lee J. Bain and Max Engelhardt, Introduction to Probability and Mathematical
Statistics
Homework Problem 4.5
Rework Exercise 3, assuming that the cards were drawn with replacement.
(Lee J. Bain and Max Engelhardt, Introduction to Probability and Mathematical
Statistics.)
Exercise 3 is repeated here for convenience.
Five cards are drawn witho
Homework Problem 4.7
Suppose that X 1 and X 2 are discrete random variables with joint pdf of the form
c ( x1 + x2 ) , x1 = 0,1, 2, x2 = 0,1, 2
f X1 , X 2 ( x1 , x2 ) =
.
otherwise
0,
Find the constant c.
(Lee J. Bain and Max Engelhardt, Introduction to
Homework Problem 2.5
A discrete random variable has pdf f X ( x ) .
1 x
, x = 1, 2,3
k
, find k .
(a) If f X ( x ) = 2
0,
otherwise
1 x 1
, x = 0,1, 2
k
(b) Is a function of the form f X ( x ) = 2 2
a pdf for any k ?
otherwise
0,
(Lee J. Bain and M