Lecture #1
27 September 2012
Amniocentesis
Risks of Downs Syndrome and Other
Chromosome Abnormalities
Age
Risk for Downs Syndrome
Risk of All Chromosome
Abnormalities
20
1 in 1,667
1 in 526
25
1 in 1,250
1 in 476
30
1 in 952
1 in 384
35
1 in 385
1 in 192
Problem Set #3
Due: 24 October 2012
MAE 271A: Probability and Stochastic Processes in Dynamic Systems
1. Problem #2, Section 2.12 of your text.
2. Problem #5, Section 2.12
3. Problem #25 a) b), Section 2.12
4. (From Pitman, 1989) Let (X, Y ) be a point ch
Problem Set #2
Due: 17 October 2012
MAE 271A: Probability and Stochastic Processes in Dynamic Systems
1. Problem #11, Section 1.6 of your text.
2. Problem #15, Section 1.6
3. Problem #17, Section 1.6
4. (From Olofsson, 2005) You roll a die and ip a fair c
Problem Set #1
Due: 10 October 2012
MAE 271A: Probability and Stochastic Processes in Dynamic Systems
1. Dene a probability space for the following events;
(a) One hand of blackjack (i.e. two cards out a deck of 52 cards)
(b) Getting hit by lightning whil
Syllabus
27 September 2012
MAE 271A: Stochastic Processes
1.
Overview
This is the rst quarter in a three-quarter sequence of courses that looks at the analysis, estimation,
and control of systems whose uncertainties are modeled with probabilities. In this
Lecture #7
18 October 2012
Gamblers Ruin
You are playing a series of games of chance
against Gambler H.
You have probability p of winning each individual
game
H has a probability q = 1-p of winning
You start with $k dollars, H starts with $N-k
dollars
Lecture #6
16 October 2012
Lets Talk About Problem Set #1
Many of you didnt know how to define a probability space.
A sample space is a set of all possible outcomes. Many of you
simply told me the size of the sample space
For the poker problem, many of
Lecture #5
11 October 2012
1
Rare Diseases
Suppose you are tested
for a rare disease
(affects 1 in 100,000
persons)
The test is 99.99%
accurate and indicates
that you have the
disease
Do You actually have
the disease?
2
You Might Be Surprised
A = Has
Lecture #4
9 October 2012
1
Birthday Problem
What is the probability
that two people in this
classroom have the
same birthday?
Would you believe that
the odds are better
than 70%?
2
Calculating the Birthday Problem
Easier to calculate the
probability t
Lecture #3
4 October 2012
How Many Times Do You Need to
Shuffle a Deck of Cards?
If you use a Riffle Shuffle, the answer is 7
A Cut Followed by an Interleaving
Just Randomly Insert Cards Brings this Number up
to 2500
Define a Random Deck As One in Whi
Lecture #2
2 October 2012
Last Time
Sets
Describing Random Events as Sets
Allows us to describe just about any problem
Probability as an Operation on Sets
This approach is so general that we will have to
restrict the types of sets that are allowable
Problem Set #1
Due: 31 October 2012
MAE 271A: Probability and Stochastic Processes in Dynamic Systems
1. Problem #19, Section 2.12 of your text.
2. Problem #40, Section 2.12
3. Problem #42 b) c), Section 2.12
4. (From Pitman, 1989) Let X be a random varia