Section 1.2: Descriptive and Inferential Statistics
Statistics: Science of conducting studies to collect, organize, summarize, analyze, and
draw conclusions from data.
Stats 1CC3
Table 1: Example of a data set (Sample data)
Lecture Notes
Name
Weight (lbs.
Stat 220: Assignment 3 - Solutions
[4]
1. Roll a fair six-sided die. Use the sample space S = cfw_1, 2, 3, 4, 5, 6. Dene events
A = cfw_1
B = A
= cfw_2, 3, 4, 5, 6
Observe that A and B are mutually exclusive. Prove that A and B are dependent.
Solution: As
MID-TERM EXAMINATION
WINTER TERM 2015
Student Name (Print Legibly)
SOLUTIONS
(family name)
(given name)
Signature
Waterloo Student ID Number
COURSE NUMBER
Stat 220
COURSE TITLE
Probability (Non-Specialist Level)
COURSE SECTION
001
DATE OF EXAM
Thursday, F
Stat 220: Assignment 5 - Solutions
1. During lunch time, students arrive at a local food court according to a Poisson process
at an average rate of one student every ve seconds.
[3]
(a) What is the probability that exactly one student will arrive in a ve
Stat 220: Assignment 1 - Solutions
1. Recall this random wheel from class:
for the experiment of spinning this wheel.
. We dened the following sample spaces
S = cfw_1, 2, 3, 4, 5, 6, 7, 8, and
S = cfw_odd, even.
[1]
(a) Give an example of a simple event (
Stat 220: Assignment 4 - Solutions
1. A local restaurant is running a contest and claims that you will have a one in six chance
of winning a prize each time that you buy a drink.
[3]
(a) Suppose you buy ve drinks in a given week. What is the chance that y
Stat 220: Assignment 6 - Solutions
[3]
1. (a) Let 0 = x R satisfy |x| < 1. Prove that
nxn =
n=0
x
.
(1 x)2
Solution: We have
nx
n
nxn1
= x
n=0
n=0
= x
n=0
= x
d
dx
d n
(x )
dx
xn
n=0
d
1
, since |x| < 1
dx 1 x
0(1 x) 1(1)
= x
(1 x)2
1
= x
(1 x)2
x
.
=
(1
Stat 220: Assignment 8 - Solutions
1. Roll two fair six-sided dice. Let X record the score on the rst die. Let Y record the
score on the second die. Dene U = X + Y and V = X Y .
[3]
(a) Compute E(U ).
Solution: As X and Y have discrete uniform distributio
Stat 220: Assignment 7 - Solutions
1. Let X and Y be discrete random variables with ranges X cfw_1, 2, 3, Y cfw_2, 3 and
with joint probability function
f (x, y) = k
[2]
1 1
+
x y
, for some constant k.
(a) Determine k.
Solution: With the given setup, we
Stat 220: Assignment 9 - Solutions
1. Let X be a continuous random variable with probability density function
f (x) =
[2]
kx(1 x) if 0 < x < 1
.
0
otherwise
(a) Determine the constant k.
Solution: For a probability model, we require
1
f (x)dx
1 =
0
1
x(1
Stat 220: Assignment 11 - Solutions
Reminder: Use a correction for continuity wherever it is appropriate and practical to do
so.
Note: Throughout these solutions, we let Z N (0, 1) whenever it is needed.
1. The lengths (in inches) of nails produced in a f
Formulas:
1. Geometric:
(a) Finite:
(b) Innite:
a(1rn )
1r
a
1r
=
2. Exponential: ex =
= a + ar + ar2 + + arn1 for r = 0.
k=0
ark = a + ar + ar2 + ar3 + ar4 + for r (1, 1).
xk
k=0 k!
+
x3
3!
+ for all x.
n(n1) 2
x
2!
+
n(n1)(n2) 3
x
3!
=1+x+
x2
2!
3. Bin
FINAL EXAMINATION
FALL TERM 2013
Student Name (Print Legibly)
(family name)
(given name)
Signature
Waterloo Student ID Number
COURSE NUMBER
STAT 220
COURSE TITLE
Probability - Non-Specialist
COURSE SECTION
001
DATE OF EXAM
Monday, December 9, 2013
TIME PE
FINAL EXAMINATION
FALL TERM 2013
Student Name (Print Legibly)
SOLUTIONS
(family name)
(given name)
Signature
Waterloo Student ID Number
COURSE NUMBER
STAT 220
COURSE TITLE
Probability - Non-Specialist
COURSE SECTION
001
DATE OF EXAM
Monday, December 9, 20
Stat 220: Assignment 2 - Solutions
1. Three numbers are chosen at random without replacement from the set
cfw_1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
[3]
(a) Compute the probability that the three numbers form an arithmetic sequence.
(Note, the order in which the
Stat 220 - Mid Term Examination 2 - Fall 2013
Solutions
Instructions:
This examination is closed book.
You have 80 minutes to complete the exam.
The problems you need to solve are on the second sheet.
Please wait to begin the exam until told to start
Section 3-3: Measure of Variation
Measures of central tendency give us measures of where the middle of a
set of data occurs, but this is not enough to characterize a set of data.
Consider the following two data sets:
Stats 1CC3
Lecture Notes
Week 3: Janua
Section 4-2: Sample Spaces and Probability
Denition: A probability experiment or a Trial is a chance process that leads to
well-dened results called outcomes. (You know all possible outcomes before performing
the experiment.)
Stats 1CC3
For eg: Tossing a
Section 4-5: Counting Rules
In order to determine the number of all possible outcomes for a sequence
of events the following three counting rules can be used.
Stats 1CC3
Lecture Notes
1. Fundamental Counting Rule
Week 5:
January 29-February 02, 2007
Secti
Section 6-4: Applications of the Normal Distribution
To nd the probability that a normal random variable X takes for given
and , for example, P (1.42 < X < 2.53), follow the steps given below
Stats 1CC3
Step 1. Find Z-score using
Lectures 8
Z =
Sections:
Appendix B.2: Bayes Theorem:
There are two boxes Box 1 contains 2 red balls and 1 blue ball. Box 2 contains 3
blue balls and 1 red ball. First, a box is selected at random and then a ball is taken out, if it
is found to be a red ball, what is the probabil
Section 7-2: CI for (when known or n 30)
Denition: A point estimate of a parameter is a specic numeric value.
The point estimate of is X.
Stats 1CC3
Denition: An interval estimate of a parameter is an interval or a range of
values used to estimate the par
Section 5-4: The Binomial Distribution
Stats 1CC3
Denition: A binomial experiment is a probability experiment which
satises
Lecture Notes
1. Each trial can have only two outcomes or can be reduced to two
outcomes, success (S) and failure (F).
Week 7: Febr
Sections 8.2 - 8.4:Hypothesis testing for the Mean
Denition: A statistical hypothesis is a conjecture about a population
parameter. This conjecture may or may not be true.
Stats 1CC3
Lecture 10
Denition: A Type-I error occurs if one rejects the null hypot
Section 8-5: z -test for proportion
Step 1. Formulate the null (H0 ) and alternate (H1 ) hypotheses.
Stats 1CC3
H0 : p = p 0
H1 : p = p 0
Lecture 11
Sections: 8.5, 9.2, 9.6
(Two-tailed test)
H0 : p p 0
H1 : p > p 0
(Right-tailed test)
H0 : p p 0
H1 : p <
Chapter 10: Correlation and Regression
Determining the relationship between variables.
Stats 1CC3
Student
Hours of study (x)
Grade (y)
A
6
82
B
2
63
C
1
57
D
5
88
E
2
68
F
3
75
Lecture 12
Sections: 10.2, 10.3, 10.4
1. Are two variables x and y related?
2.
Chapter 2: Frequency Distributions and Graphs
When data are collected in original form, they are called raw data.
To describe situations, draw conclusions, or make inference about events, raw data must
be organized in some meaningful way. The most conveni
Stat 220: Assignment 11
(Do Not Hand In, Solutions will be posted on 2015-04-08)
Reminder: Use a correction for continuity wherever it is appropriate and practical to do
so.
1. The lengths (in inches) of nails produced in a factory are normally distribute