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 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
Lecture 21:
Multiple Random Variables
CEE 11@UCI
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 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 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 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
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
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
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
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 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
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
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 #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