Discrete random variables
CEE 11 ch 3
Copyright Dr. Brigitte Baldi 2011
Random variables
A random variable X is a function that associates a unique numerical
value with every outcome of a random experiment.
A discrete random variable can take only a fini
Lecture 25
CEE 11, Probability and Sta8s8cs
Professor Stanley B. Grant
Sta8s8cal Inference is used for
Point es)ma)on
Hypothesis tes8ng
Interval es8ma8on
Determining and valida8ng probability
distribu8ons (+/-)
Method
Lecture 24
CEE 11, Probability and Sta8s8cs
Professor Stanley B. Grant
Sta8s8cal Inference is used for
Point es)ma)on
Hypothesis tes8ng
Interval es8ma8on
Determining and valida8ng probability
distribu8ons (+/-)
Point
Lecture 21:
Multiple Random Variables
CEE [email protected]
Professor Stanley Grant
Guest Lecturer: Asal Askarizadeh
1
From Previous Lecture:
Random Variable:
Mathematical expression of an event in analytical form
2
Multiple Random Variable
Event is a result of two
Lecture 20
CEE 11, Probability and Sta8s8cs
Professor Stanley B. Grant
Summary: Discrete Time or Space
Binomial Distribu/on PMF
P X = k;n, p = n p k 1 p
k
!
(
)
(
)
nk
Summary: Discrete Time or Space
Binomial Distribu/on
CEE 110 - Methods III: Modeling, Economics, and Management
Spring Quarter 2017
Homework 6 (Class Project) [Full credit = 40 pts]
Due Friday of week 10, June 9th at noon in the CEE110 mailbox in the Gateway (no
extension)
Up to five people can form a group
Problem 1
Legend:
ES
Act.
EF
LS
Dur.
LF
You can use the legend I design here, the one in the lecture, or any
other type designed by yourself. The legend is not fixed.
6
3
5
C
13
5
8
13
13
D
14
15
1
16
A
4
13
E
15
1
4
5
13
2
15
1
F
18
16
3
19
7
19
H
25
19
HW#3 Solution
1.
(a)
Payoff table
High interest
Medium interest
Low interest
Plan I
220
170
110
Plan II
200
180
150
Note that the goal here is to attract as many qualified students as possible, so we treat the number of
students as profit. When we input t
Lecture 26
CEE 11, Probability and Sta8s8cs
Professor Stanley B. Grant
Sta8s8cal Inference is used for
Point es8ma8on
Hypothesis tes+ng
Interval es8ma8on
Determining and valida8ng probability
distribu8ons (+/-)
Hypothe
Lecture 23
CEE 11, Probability and Sta8s8cs
Professor Stanley B. Grant
General Beta Distribu8on
Appropriate for situa8ons where the random
variable (or possibility space) takes on a nite range
of values (from X = a
CEE 11 Lab #1 (Due in EEE Dropbox by 11:55pm Monday, Week 5)
Name: Talal Ammouri
ID:
15089376
Instruction: First attach a small object (for example a wrap of scotch tape) to the head of a coin. Then th
CEE 11 Lab #2 (Due in EEE Dropbox by 11:55pm Monday, Week 8)
Name:
Talal Ammouri
ID:
15089376
Instruction: Toss a fair coin for 100 times.
H=head, T=tail
Q1. The number of heads is
53
the number of
CEE 11 Lab #3 (Due in EEE Dropbox by 11:55pm Wednesday, Week 10)
Name:
Talal Ammouri
ID:
15089376
Q1: From results in Q2 of Lab 1, what is your point estimate of = ()?
p = P(head) = 0.54
Q2: From results
The Judicial Branch:
Mere Interpreter or
Equal?
Intro to American Government Week 9 Slides
The Structure of the Judicial Branch
There are many courts as a part of the (federal) judiciary.
Roughly, three types
i) Supreme Court: Only court required by Co
The U.S. Senate:
An Affront to
Democracy?
Intro to American Government Week 8 Slides
The Effects of a Bicameral Legislature
Recall from last week: Any bill must pass both houses
(House and Senate) to become a law.
This creates twice as many places for a
The U.S. President:
Leader of the Free
World?
Intro to American Government Week 10 Slides
Constitutional Powers of the Presidency
Founders wanted a balanced presidency:
Strong enough to avoid anarchy, weak enough to prevent tyranny.
Many different cons
Assignment 2
CEE11, Spring 2016
(1) Cement and reinforcing steel (rebars) are essential materials for constructing a reinforced
concrete building. During construction, the probabilities of encountering shortages of these materials
(e.g., caused by strikes
Lecture 22
CEE 11, Probability and Sta7s7cs
Professor Stanley B. Grant
Hypergeometric Distribu7on
Useful in Quality Assurance/Quality Control
Hypergeometric Distribu7on
Useful in Quality Assurance/Quality Control
Imagine