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
Instr
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 an
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 functi
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 variab
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 fy
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
~ 2%)
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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()
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
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):
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
MA240 Week 4 Lab Notes
Probability and Two-Way Tables
To describe data we often use frequencies. Two-way tables are a way to display frequencies of events and how they
interact with other events:
# of
MA240 Lab Notes - Week 2
Text Reference: 1.1-1.3
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
Rela
MA240 Lab Notes - Week 3
Text Reference: 1.4-1.6
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 e
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 All
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,
E-Mail: dwo
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 va
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 approxima
The Normal Distribution
Overview
Normal distributions
The 68-95-99.7 rule
The standard Normal distribution
Using the standard Normal table
Normal calculations & probabilities
Normal approximation to t
Sep10
September-10-13
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