1) Lecture 1: General
A. Positive question Why is some feature the way it is>
B. Normative question What should some feature be?
C. Quantities we often use:
C.i. Households: Consumption, Savings, Hour
214 Exam 1
1) Lecture 1: Introduction
A. Quality attributes describe the codes fitness for further development/use:
reuse code, easy to change, easy to add
B. Objects support simulation, extensibility
21257 Test 1 Notes
1.
Chapter 1.4 Solving LP Graphically
a. Make constraints equalities, and graph the corresponding lines
b. Shade in graph to match inequality constraints
c. Find the corners
d. Eva
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November
December
January
February
March
52.79
52.79
58.13
58.13
57
28.5
38.39
19.195
98.73
49.365
71.25
35.625
376.29 243.605
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52.79
58.13
28.36
57
23.55
38.39
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Lab 1 TV Jammer
* Please read and understand the Lab Readiness Prerequisites and
Lab Etiquette and Procedures documents before starting this lab *
1. Introduction
In this lab you will build the core p
Lecture III24 January 2012
36217
Liz Kulka
Readings: 1.1, 1.2, 1.6
1
Review
Given a sample space , a probability law or distribution P is a function dened over subsets of
such that:
1. P(A) 0 A
2.
Lecture IV26 January 2012
36217
Liz Kulka
Readings: 1.6
1
Counting Methods
Discrete Uniform Distribution: If is nite and all points in are equally likely, then
Pr(A) =
A
A

This is a type of Rand
Lecture V31 January 2012
36217
Liz Kulka
Readings: 1.3  1.5
1
Conditional Probability
Recall the scenario where we took some medicine that had possible side eects.
A = cfw_I will experience side eec
Lecture VI2 February 2012
36217
Liz Kulka
Readings:
1
Recall
Pr(AB) =
Pr(A B)
Pr(B)
(Will be on the exam!)
P a probability on and A1 , A2 , . . . , An a partition of with P (Ai ) > 0) i.
Law of Tota
Lecture VII7 February 2012
36217
Liz Kulka
Readings:
Midterm 1 in 10 days, no notes and no calculators permitted.
There will be a handout on BB with equations that we do not need to memorize.
The for
Lecture VIII9 February 2012
36217
Liz Kulka
Readings:
1
Random Variables, Continued
1.1
Review
Random Variables X : R
Range(X) is the set of all possible values of X
pmf (probability mass function
Lecture IX14 February 2012
36217
Liz Kulka
Readings: Section 2.4
Material through this lecture will be on Exam 1.
1
Discrete Random Variables
X Bernoulli(p)
X Binomial(n, p)
0<p<1
X Geometric(p)
X N
Lecture X21 February 2012
36217
Liz Kulka
Readings:
Midterm 1 Scores:
Score
Percentage of Class
> 90
53%
80 90
16%
70 80
17%
60 70
5%
< 60
9%
1
Expectation
Let X be a random variable with pmf pX
Lecture XII28 February 2012
36217
Liz Kulka
Readings:
1
Conditional Expectation
Given two rvs X and Y , the conditional expectation of X given Y is the rv E[XY ] obtained as a
function f (Y ) of Y s
Lecture XIV6 March 2012
36217
Liz Kulka
Readings:
1
Continuous Random Variables (Lots of Integrals!)
Note: reviewing integrals would be a good idea.
A random variable X is continuous if its range is
Lecture XV8 March 2012
36217
Liz Kulka
Readings:
1
Continuous Random Variable
X is a continuous RV when Pr(X A) =
A fX (x)dx
A R. fX is the pdf of X
1. fX (x) 0 x
2.
+
fX (x)dx
cdf of X: FX (c) =
=
Lecture XVI20 March 2012
36217
Liz Kulka
Readings:
Midterm II: March 29 (next Thursday). Will cover everything since Midterm I.
1
Continuous Random Variable
A random variable X is continuous if there
Lecture XVII22 March 2012
1
36217
Liz Kulka
Review of Integration
Let a b +:
b
xc dx =
a
b
1
xc+1
c+1
c
f (x)dx =
a
b
(1)
a
b
f (x)dx +
a
f (x)dx if a < c < b
(2)
c
b
b
cf (x) + dg(x)dx =
a
b
cf (x)d
Lecture XVIII27 March 2012
1
36217
Liz Kulka
Joint, Marginal and Conditional pdf s
X, Y are uniformly distributed over set A R2
4
A
3
2
L
1
1
2
3
4
1
4
fX,Y (x, y) =
0
(x, y) A
o.w.
Pr(X, Y ) S) =
fX
Lecture XXI10 April 2012
1
36217
Liz Kulka
Markov Chains
A stochastic process in discrete time is a sequence X0 , X1 , . . . of random variables.
1.1
Trivial Cases
X0 , X1 , X2 are iid from a common
Lecture XX5 April 2012
1
36217
Liz Kulka
Covariance
Let X and Y be two rvs. The covariance of X and Y is
Cov [X, Y ] = E [(X E [X])(Y E [Y ])]
If Cov [X, Y ] > 0 X and Y tend to move together:
y
x