Fall Term, 2012
Name: gaLwzA/gl
Student Number:
Section:
WILFRID LAURIER UNIVERSITY
Waterloo, Ontario
Mathematics 240 Introduction to Probability and
Statistics
Midterm October 29, 2012
Instructor: G. Campolieti
Time Allowed: 80 minutes
Total V
MA240 MIDTERM INFORMATION
Date and time: Monday, March 4, during your lab.
Content: The midterm covers up to, and including, the material in the lecture on Wednesday,
February 13, specically, up to and including the material on the Normal Distribution. Th
MA240 STUDY GUIDE (WINTER 2013) WEEK 7
1. Bivariate Probability Distributions. (February 25)
Reading assignment: Chapter 4.1
After reading this, you should be able to do the following.
Given a function of two variables, determine whether or not it is a j
MA240 Week 11 Lab Notes
Several Independent Random Variables
A random sample of size n is a collection of n distinct random variables. If random variables X1 ; X2 ; :; Xn are
independent random variables then:
1. The joint p.m.f. (or p.d.f) is the product
MA240 Week 9 Lab Notes
Joint Probability Mass/Density Functions:
1. Of the Discrete Type:
Consider two discrete random variables X with possible values fx1 ; x2 ; :; xn g and Y with possible
values fy1 ; y2 ; :; ym g. Then f (x; y) is the joint probabilit
Exploring and Describing Distributions
Using Sample Statistics
(Ch. 3.1 & 3.2 plus supplementary material)
Contents
Types of statistics
Individuals, populations and samples
Variables
quantitative vs. categorical
discrete vs. continuous
nominal vs. o
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Introduction to R
1. Opening and Closing R
R is opened using the icon on your computer. Alternatively, you can nd it in the program les from the start menu of
your computer.
R is closed using the q() command or by clicking the `X' in the top right corner
MA240 Week 7 Lab Notes
Continuous Random Variables and Probability Density Functions (p.d.f.s):
For continuous random variable X having possible values over a continuous interval [i.e., the reals], we are
interested in the probability the variable takes o
MA240 Week 10 Report The Normal Distribution
Name:
Student Number:
Lab:
Fall 2013
1. [12 marks] Suppose the random variable Z is normally distributed with mean uZ = 0 and standard deviation
N (0; 1):
Z = 1: That is, Z
(a) For each of the following, use Ta
MA240 Week 12 Report Con dence Intervals
Name:
Student Number:
Lab:
Fall 2013
1. [7 marks] *ANSWERS WILL VARY, WITHIN REASON, FOR #1(b),(c)*
(a) Suppose X N (250; 225): Use R and the code samp1<rnorm(40,250,15) to generate a random sample
of size 40 from
MA240 Week 4 Lab Notes
Probability and TwoWay Tables
To describe data we often use frequencies. Twoway tables are a way to display frequencies of events and how they
interact with other events:
# of B
# of B 0
Total
# of A
a
c
a+c
Then, for example, P (
MA240 Lab Notes  Week 2
Text Reference: 1.11.3
On Frequencies and Histograms (1.1)
Frequency the number of times a certain outcome occurs in a nite number of repetitions of a random experiment
Relative Frequency  the ratio of the frequency of an outco
MA240 Lab Notes  Week 3
Text Reference: 1.41.6
Conditional Probability (1.4)
Consider the events A and B where P (B) > 0. Then the probability of A given that the condition(s) of
event B are satis ed [i.e., the conditional probability of A given B] is:
Fall Term, 2013
Name: 50Lu77o/u .3
WILFRID LAURIER UNIVERSITY
Waterloo, Ontario
MA240 a Introduction to Probability and Statistics
Midterm October 30, 2013
Instructor: Dr: D. iVooUbrd
Time Allowed: 80. reneries
Total Value: 65 mar/ts
Number of P
Fall Term, 2013
Mathematics 240A/C Introduction to Probability and Statistics
Department of Mathematics, Faculty of Science, Wilfrid Laurier University
Instructor:
Dr. Douglas G. Woolford,
EMail: dwoolford@wlu.ca, Office: BA528 (Bricker Academic), Teleph
MA240 STUDY GUIDE (WINTER 2013) WEEK 6
1. Exponential and Gamma Distributions (February 11)
Reading assignment: Chapter 3.5
After reading this, you should be able to do the following.
For a random variable X which has the exponential distribution, determ
Sampling Distributions
How have we answered questions like:
What are the chances of getting 5 heads in 20 tosses of
a coin?
If infections from a certain disease occur at an average
rate of approximately 9 a month, what is the likelihood
that there will
The Normal Distribution
Overview
Normal distributions
The 689599.7 rule
The standard Normal distribution
Using the standard Normal table
Normal calculations & probabilities
Normal approximation to the Binomial
2
Normal Distributions
a continuous distri
Sep10
September1013
11:31 AM
1.0
10 flips of a fair coin: There is lots of variability when the sample size is small.
2/2
2/3
0.6
empirical probability
0.8
1/1
3/6
0.4
2/4
3/7
2/5
4/10
3/9
0.0
0.2
3/8
2
4
6
8
10
number of flips
0.0
0.2
0.4
0.6
empirical

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Fall Term, 2012
Name: SOLWT/OA/S
Student Number:
WILFRID LAURIER UNIVERSITY
Waterloo, Ontario
Mathematics 340 Probability Theory
Test I 5:30  6:50 pm, Thursday, October 18, 2012
Instructor: Dr. G. Campolieti
Time Allowed: 80 minutes
Total Value: 100 ma
Fall Term, 2012
Name: SOLUTIONS
Student Number:
WILFRID LAURIER UNIVERSITY
Waterloo, Ontario
Mathematics 340 Introduction to Probability Theory
Test II ~ November 22, 2012
Instructor: Dr. G. Campolieti
Time Allowed: 80 minutes
Total Value: 100 marks
Num
Fall Term, 2009
Name:
Student Number:
WILFRID LAURIER UNIVERSITY
Waterloo, Ontario
Mathematics 340 Introduction to Probability Theory
Test I October 20, 2009
Instructor: Dr. R. Makarov
Time Allowed: 80 minutes
Total Value: 100 marks
Number of Pages: 6 plu