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