Mathematics Department
Probability & Statistics Science
201 BZS 05
COURSE OBJECTIVES
For details, see Dawson Science Program.
COURSE COMPETENCIES
This course will allow the student to fully achieve the competency:
00UV: To apply the methods of descriptive

Inferences Concerning Contingency Tables
Suppose we asked 300 students whether he or she preferred taking liberal
arts courses in the area of math-science, social science, or humanities. The
results are broken down in the following chart.
Favourite Subjec

Example: This semester there were seven sections of a particular math
course at Dawson. Does the data indicate that the students had a preference
for certain sections?
Section
Number of students
1
2
3
4
5
6
7
18
12
25
23
8
19
14
In the previous example we

Dawson College: Probability and Statistics: 201-BZS-05
Formula Sheet
x f
x
=
n
n
x =
SS(x) =
s2 =
2
(x x)
SS(x)
n1
=
x
s=
s2
Chebyshevs Theorem: 1
2
2
n(x)
( x)2
=
= x
n
2
z=
( x f )2
x f n
2
x
s
1
y2
SS(xy) = (x x)(y y) = xy
( x) ( y)
n
SSE = (y y)
2

Statistical Methods
Final Exam December 2013
_
Part I (One mark each)
Answer true if the statement is always true. Answer false otherwise.
1. If X is a binomial random variable, then E ( X 2 ) (np)2 np(1 p)
2. Increasing the value of
(all else remaining u

Formula Sheet for Statistical Methods (201-DDD-05)
Five number summary:
min, Q1 , median, Q3 , max
Q1 : median of smallest half
Q3 : median of largest half
Fourth spread
fs = Q 3 Q 1
Outliers
xi is an outlier if its distance from the
closest fourth (Q1 or

Example: A factory has two assembly lines. One line is older, slower and less
reliable than the other.
On a given day the older assembly line assembled 8 products of which 2 were
defective and six non-defective.
On the same day the newer assembly line has

Normal Approximation to the Binomial
Recall that for a binomial distribution
and
and the random variable x was the number of successes in n trials.
If
(the probability of a success for one trial is 0.5) then
should be right in the middle of the possible x

D
M
epartment of
athematics
Final Examination
May 21, 2013
14h17h
Statistical Methods
201-DDD-05
Instructors: Olivier Dubois, Moushira Guindi
Student name:
Student number:
Instructor:
Instructions
1. Do not open this booklet before the examination begins.

The t-distributions
In our previous examples we assumed that the standard deviation of a
population was known but in most cases neither
or
is known.
If we don't know it seems natural to use sample standard deviation , but
this will result in less accurate

The Operating Characteristic Curve
Here we discuss type II errors. The probability of accepting false null
hypothesis will be denoted by .
We can calculate
corresponding to specific alternate values
.
Recall the coffee dispenser example: A coffee dispense

Chi-Square Statistic
A multinomial population is a population with a single characteristic of interest
but more than two possible results.
For example we can view an election as
Binomial
probability of voting liberal
probability of not voting liberal
Mult

Final Exam
201-DDD-05
May 26, 2014
1. For the survey question How many universities did you apply to?, the data obtained is summarized below in a frequency
table. A total of 47 students answered this question.
Number of universities
Frequency
0
6
1
6
2
19

Dawson College
Mathematics Department
Final Exam
201-BZS Probability & Statistics
Instructor: J. Graham
2 5 p.m.
December 18, 2009
Instructions: There are 10 questions of equal value. Round all probability and proportion final
answers to 4 decimal places.

DAWSON COLLEGE DEPARTMENT OF MATHEMATICS
201-BZS-05
PROBABILITY AND STATISTICS
Final Exam
MAY 23rd, 2012
M.MARCHANT, K. AMEUR
Name:_
Student ID:_
Grade:_
Please show all work and justify all answers.
The test is printed on both sides of the sheets.
Ins

Dawson College: Probability and Statistics: 201-BZS-05
Last Name:
_
First Name:
_
Student ID:
_
Assignment 1
Please answer all of the following questions in the space provided. Write clearly and make sure
to use correct notation. Please state any variable

Dawson College: Probability and Statistics: 201-BZS-05
Formula Sheet
x
x f
x =
=
n
n
SS(x) =
s2 =
(x x)2 =
SS(x)
n1
s=
s2
x2
p0 = p
n = (z(/2)2
d = d
s
sx1 x2 =
s1 2
n1
s1 4
n1 2 (n1 1)
s
E = z(/2)
+
s2 2
n2
+n
2
sd =
s1 2 s2 2
+
n1
n2
( fi ei )2
=
e

Dawson College: Probability and Statistics: 201-BZS-05
Formula Sheet (Test 2)
E(x) = n p
= xP(x)
2 = (x )2 P(x) = x2 P(x) 2
P(x) = nCx px qnx
P(x) =
1 x 2
e 2 ( )
y = f (x) =
2
x
x =
n
x
n
or
E = z(/2) x
z(/2) x
E
2
x (za + z )
n=
0 a
2
n=
r
N n
N 1

201-DDD-05
FINAL EXAM
Fall 2012
1. Last year, during a lecture, I asked my students: How many text messages did you send today so
far? (It was about noon.) Here is a stem-and-leaf plot showing the data I obtained.
0
1
2
3
4
7
8
10
11
00000001133455777
000

Final Exam
J. Graham
Dawson College
Math BZS
Dec. 14, 2012
Probability & Statistics
Q1. A cumulative frequency
polygon is shown here.
a) Sketch the corresponding
relative frequency polygon.
b) Estimate the mean of the
sample.
cumulative frequencies
Instru

Answers for DDD Winter Final2013
1)
2a)
3)
4a)
E(x)=98.6, V(x)=12.96, s=3.6
0.0625
b) 0.445
c) 0.4375
0.12
0.384 b) 0.2
d) 0.04
3(x 100) 2
if 0 x 100
5)
a) 0.721 b)20.6299km/h
c) f (x) F (x)
1003
0
otherwise
6a) p(1)=0.0769, p(2)=0.3297, p(3)=0.4396, p(4)

Answers to DDD Final Fall 2013.
Part I:
1. T
2. F 3. T 4. T 5. T
Part II:
1. k=0.67 or k=0.03
2. k=6
3. 0.464
4. 0.9783
5. N=40
6. N=495
7. Z=2
8. E(X)=6, E(Y)=25
9. 0.7813
Part III
1. 0.001
2. a) 270725
b) 118807
c) 188474
d) 92820
e) 0.0106
3. P( F3 | M

Dawson College: Probability and Statistics: 201-BZS-05
Formula Sheet
x
x f
(class mark) f
=
n
n
n
x =
SS(x) =
(x x)2 =
=
s2 =
x2 f
SS(x)
n1
x2 n(x)2 =
( x f )2
n
s=
( x)2
n
(class mark)2 f
s2
Chebyshevs Theorem: 1
x2
z=
(class mark) f )2
n
xx
s
1
y

The Poisson Distribution
A Poisson experiment is characterized by the following properties:
1) The number of successes that occur in any interval is independent of the
number of successes that occur in any other interval
2) The probability of a success is

Critical Values of z
Some notation:
We will let
(sometimes written
of
lies to the right of
.
For example, if
) be the z-score such that an area
then we have the following situation
will refer to the area at both tails of the normal curve. For example
woul

Inferences Concerning the Difference Between Proportions
(Independent Samples)
Recall that we can measure elements of a population in terms of a qualitative
property by looking at the proportion of the population that has the specific
quality.
We will use

Dawson College: Probability and Statistics: 201-BZS-05
Last Name:
_
First Name:
_
Student ID:
_
Assignment 2
Please answer all of the following questions in the space provided. Write clearly and make sure
to use correct notation. Please state any variable

Continuous Random Variables
We have seen a few examples of probability distributions so far but the single
most important probability distribution to statisticians is probably the normal
probability distribution.
The normal probability distribution has a