STA257: Probability and Statistics 1
Instructor: Katherine Daignault
Department of Statistical Sciences
University of Toronto
Week 3
Outline
Random Variables  Discrete (Chapter 2.1)
Quick Calculus Review
Discrete Random Variables
Bernoulli Random Variables
Binomial Distribution
Geometric Distribution
Negative Binomial Distribution
Hypergeometric Distribution
Poisson Distribution
Outline
Random Variables  Discrete (Chapter 2.1)
Quick Calculus Review
Discrete Random Variables
Bernoulli Random Variables
Binomial Distribution
Geometric Distribution
Negative Binomial Distribution
Hypergeometric Distribution
Poisson Distribution
Calculus for this week
I
Starting from today, we will be using material that has been
taught in Calculus 1 and 2 courses.
I
I will quickly refresh what you should be familiar with as you
need them.
I
This week, you will need to step functions, limits, how to work
with a series, as well as the Geometric series.
Working with a Series
I
Geometric Series
I
One series that we will be using today is the Geometric series,
or rather a lemma related to it.
I
A Geometric series is any series of the form
∞
X
n
=1
az
n

1
=
∞
X
n
=0
az
n
I
Lemma: If

z

<
1 then
∑
∞
k
=
l
z
k
=
z
l
1

z
I
i.e. the Geometric series converges when

z

<
1 to the value
above
Outline
Random Variables  Discrete (Chapter 2.1)
Quick Calculus Review
Discrete Random Variables
Bernoulli Random Variables
Binomial Distribution
Geometric Distribution
Negative Binomial Distribution
Hypergeometric Distribution
Poisson Distribution
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 Summer '08
 HADASMOSHONOV
 Probability theory, Binomial distribution, Discrete probability distribution, Geometric distribution, Hypergeometric Distribution