Correlation and causation (p. 179)
-high correlation between #sodas sold in year and #divorces, years 1950-2010. Does that mean
that having more sodas makes you more likely to divorce?
Over that time, population increased, so changes in both variables are
Ladder of powers (p. 269)
Power Name
Notes
2
Square of values Left skewed
1
Unchanged data
0.5
Square root
Counted stuff; frequency
0
Logarithm
% change matters (no negative)
-0.5
+/-1/square root Rare -> direction
-1
+/-1/data
Ratio of 2 quantities wrong
Chapter 8: Linear regression finding the best line (p. 198)
In math, straight line relationship looks like y=a+bx
where x and y are variables, and a and b are numbers that describe what kind of straight line you
have.
a = intercept: value of y when x=0
Chapter 3: Displaying and describing categorical data (p. 20)
In 1991 and again in 2001, a poll was taken of 1015 adults about their opinions on working
parents. The question was considering the needs of adults and children, what do you see
as the ideal f
Chapter 13: Experiments and Observational Studies (p. 341)
How do you find out if exercise helps insomnia?
look at a bunch of people, find out if they exercise and how much, ask them to rate their
insomnia.
Suppose the people who exercise more suffer le
Week 4 9/23 Tues
Chapter 7: Scatterplots, association and correlation (p. 168)
Now look at two quantitative variables.
First tool: scatterplot.
Plot values of two quantitative variables against each other.
e.g. The airport in Oakland, California record
Chapter 11: Understanding Randomness (p.300)
What does random mean?
In short term, unpredictable
In long run, predictable:
coin: should win about 1/2 of the time.
die: should win about 1/6 of the time.
Computer random numbers generated by non-random
Chapter 14: From randomness to probability (p. 376)
Randomness
In short term, unpredictable
In long run, predictable:
coin: should win about 1/2 of the time.
die: should win about 1/6 of the time.
Tim Horton's? Dont know
Empirical probability/ random
Ch 4: Displaying and summarizing quantitative data (p.49)
Distribution -> Mostly quantitative variables slices up all the possible value of the variable into
equal width bins and gives the number of values falling into each bin
Histogram
-Bins/ classes ->
Things vary:
people are different
can't see everything or measure it all
what we can measure might be inaccurate
Ch 2: Data (p. 7)
Airlines monitored for safety and customer service. For each flight, carriers must report:
flight number
type of aircra
Chapter 5: understanding and comparing data (p. 88)
Review: Data 10, 11, 14, 15, 17, 19, 21, 28, 35:
why is median 17?
N=9; medians is (9+1)/2= 5th
find Q1 and Q3
Q1= median of 10,11,14,15,17= 14
Q3= median of 17, 19, 21, 28, 35= 21
find interquartile
Chapter 6: The standard deviation as a ruler and the normal model (p. 121)
Which is the better exam score?
67 on exam A with mean 50 and SD 10
62 on exam B with mean 40 and SD 12?
What do you say to these:
67 is better because 67 > 62? No, because mean
Chapter 12: Sample surveys
Examine a part of the whole (p.315)
Population = everyone we want to investigate.
Sample that represents/selected from population
Sample survey: ask questions of a small group of ppl in the hope of learning sth about the
entir
STAB52 - An Introduction to Probability (Week 6)
Danny Cao
STAB52 - An Introduction to Probability
Week 6 Lecture Notes
2.7 Joint Distributions
We have now studied, rather extensively, the probabilistic behaviour of a single random variable. The
next issu
STAB52 - An Introduction to Probability (Week 5)
Danny Cao
STAB52 - An Introduction to Probability
Week 5 Lecture Notes
2.6 One-Dimensional Change of Variables
In the past two weeks, we familiarized ourselves with random variables and their distributions.
STAB52 - An Introduction to Probability (Week 1)
Danny Cao
STAB52 - An Introduction to Probability
Week 1 Lecture Notes
1.1 Probability: A Measure of Uncertainty
Probability is a mathematical approach towards quantifying and understanding uncertainty. Pro
STAB52 - An Introduction to Probability (Week 4)
Danny Cao
STAB52 - An Introduction to Probability
Week 4 Lecture Notes
Example (Matching socks)
Suppose that you have 3 white left-footed socks and 7 white right-footed socks in the dryer amongst other
arti
STAB52 - An Introduction to Probability (Week 3)
Danny Cao
STAB52 - An Introduction to Probability
Week 3 Lecture Notes
2.1 Random Variables
Denition 1.2.1 A random variable is a function from the sample space S to the real number line R.
What we mean by
STAB52 - An Introduction to Probability (Week 2)
Danny Cao
STAB52 - An Introduction to Probability
Week 2 Lecture Notes
Here are four more combinatorics problems to further your understanding of the topic:
Example (5 card hands)
Suppose we are dealt ve ca
STAB52 - An Introduction to Probability (Week 11)
Danny Cao
STAB52 - An Introduction to Probability
Week 11 Lecture Notes
4.1 Sampling Distributions
Suppose that X1 , ., Xn are independent and identically distributed (i.i.d.) random variables. cfw_X1 , .,
STAB52 - An Introduction to Probability (Week 10)
Danny Cao
STAB52 - An Introduction to Probability
Week 10 Lecture Notes
3.5 Conditional Expectation
In our original discussion of conditional probability, we saw how conditioning on a certain event can
cha
STAB52 - An Introduction to Probability (Week 9)
Danny Cao
STAB52 - An Introduction to Probability
Week 9 Lecture Notes
3.3 Variance, Covariance and Correlation
Last week we discussed the idea of a expectation for both discrete and absolutely continuous r
STAB52 - An Introduction to Probability (Week 7)
Danny Cao
STAB52 - An Introduction to Probability
Week 7 Lecture Notes
2.8 Conditioning and Independence
Last week, we discussed the joint distribution of two random variables X and Y . This week, we will i
STAB52 - An Introduction to Probability (Week 8)
Danny Cao
STAB52 - An Introduction to Probability
Week 8 Lecture Notes
In this lecture, we will introduce the next major topic of this course, expected value (or expectation). We
motivate the idea of expect
University of Toronto Scarborough
STAB22 Midterm Examination
March 2008
For this examination, you are allowed one handwritten letter-sized
sheet of notes (both sides) prepared by you, a non-programmable,
non-communicating calculator, and writing implement
University of Toronto Scarborough
STAB22 Midterm Examination solutions
June 2007
This examination contains a mixture of short-answer and multiple choice questions. For
the short-answer questions, write your answers in the spaces provided; for the multiple
University of Toronto Scarborough
STAB22 Final Examination
December 2010
For this examination, you are allowed two handwritten letter-sized sheets of notes
(both sides) prepared by you, a non-programmable, non-communicating calculator,
and writing impleme
University of Toronto Scarborough
STAB22 Final Examination
December 2009
For this examination, you are allowed two handwritten letter-sized
sheets of notes (both sides) prepared by you, a non-programmable,
non-communicating calculator, and writing impleme
University of Toronto Scarborough
STAB22 Final Examination
April 2009
For this examination, you are allowed two handwritten letter-sized
sheets of notes (both sides) prepared by you, a non-programmable,
non-communicating calculator, and writing implements
University of Toronto Scarborough
STAB22 Midterm Examination
October 2009
For this examination, you are allowed one handwritten letter-sized
sheet of notes (both sides) prepared by you, a non-programmable,
non-communicating calculator, and writing impleme