Stat 100 -Intro Probability
Homework 10
J. Sanchez
UCLA Department of Statistics
PROVIDE THE INFORMATION REQUESTED IN THIS BOX:
LAST NAME: FIRST NAME: ID:
TODAYs DATE:
Name of your TA : ; Time of TA session:
Instructions
(1) YOU MUST WRITE YOUR ANSWERS
Ax l
[I x. y) M
= Li: 3
FIGURE 14.18
The volume of the solid region is .
Seetlon 14.2 I Double Integrals and Volume 937
The following theorem was proved by the Italian mathematician Guido Fubini
(1879-1943). The theorem states that if R is a vertically or
Notes
The Bivariate Normal density. Summary
Juana Sanchez
jsanchez@stat.ucla.edu
UCLA Department of Statistics
ccle.ucla.edu
J. Sanchez
Joint densities: Bivariate Normal
Outline
Notes
I. Joint bivariate normal.
II. Marginal distributions derived from a jo
Stat 100 -Intro Probability
Homework 9
J. Sanchez
UCLA Department of Statistics
PROVIDE THE INFORMATION REQUESTED IN THIS BOX:
LAST NAME: FIRST NAME: ID:
TODAYs DATE:
TAs NAME: , TIME OF YOUR TA SESSION:
Instructions
(1) YOU MUST WRITE YOUR ANSWERS IN
Stat 100A/Sanchez
Practice with continuous random variables.
Review integrals for one variable from a Calculus book. Polynomials and exponentials
and constant functions, and integration by parts. Give some examples of each. This will
help you review integ
Stat 100A. Intro Probability /Sanchez
Practicing with the Normal curve
UCLA Dept of Statistics /
LAST NAME_ FIRST NAME:_ ID: _DATE:_
1.- Find
(a) The 75th percentile of the Standard Normal distribution is z =
(b) The probability that z is less than 0.45 i
Stat 100 -Intro Probability
Worksheet
J. Sanchez
UCLA Department of Statistics
LAST NAME: FIRST NAME: DATE:
TA SESSION:
Problem 1. The Intel Fiasco.
In October 1994, a flaw was discovered in the Pentium Chip installed in many new personal computers. The
Stat 100A -Intro Probability
J. Sanchez
UCLA Department of Statistics
Problem 1. (a) Prove that if Y = kX, X a random variable and k a constant, then E(Y) = kE(X) and Var(Y) =
k2 Var(X). Show work.
(b) If X is a Poisson random variable with expected value
Stat 100A/Sanchez
Review of applications of the CLT and of exact distributions of sums
1.Student scores on exams given by a certain instructor have mean 74 and standard
deviation 14. This instructor is about to give two exams, on to a class of size 25 and
Conditional Probability & BayesRule
Elisa Long
UCLA Anderson School of Management
In this class, we assume a Bayesian perspective when thinking about probabilities. In a
nutshell, this means that the probability of an uncertain event occurring is a degree
Probability Rules
Elisa Long
UCLA Anderson School of Management
A. Probability Experiments
An experiment (eg, die roll, coin toss) is an activity or procedure that produces distinct,
well-dened possibilities called outcomes. Outcomes are the nest grain; t
Notes
Partitions of the Sample Space, Axioms of
Probability, Properties
Juana Sanchez
jsanchez@stat.ucla.edu
UCLA Department of Statistics
J. Sanchez
Partitions of the Sample Space, Axioms of Probability, Properties
Outline
Notes
I. Extension of Union and
Notes
Stat 100A. Introduction to Probability
Introduction to Sample Spaces and probability when the
outcomes are equally likely.
Juana Sanchez
jsanchez@stat.ucla.edu
UCLA Department of Statistics
ccle.ucla.edu
J. Sanchez
Stat 100A. Introduction to Probabi
Notes
Introduction, Sample Space, Events
Juana Sanchez
jsanchez@stat.ucla.edu
UCLA Department of Statistics
ccle.ucla.edu
J. Sanchez
Introduction, Sample Space, Events
Announcements
Notes
The rst day of class we went over some examples of applications of
Chapter 1
Introduction
1.1
Basic System Elements
Queues (or waiting lines) help facilities or businesses provide service in an
orderly fashion. Forming a queue being a social phenomenon, it is benecial
to the society if it can be managed so that both the
Stat 100 -Intro Probability
Homework 1
J. Sanchez
UCLA Department of Statistics
PROVIDE THE INFORMATION REQUESTED IN THIS BOX:
LAST NAME: FIRST NAME: ID:
TODAYs DATE:
TAs NAME: , TIME OF YOUR TA SESSION:
Instructions
(1) YOU MUST WRITE YOUR ANSWERS IN
Stat 100 -Intro Probability
Homework 1
J. Sanchez
UCLA Department of Statistics
PROVIDE THE INFORMATION REQUESTED IN THIS BOX:
LAST NAME: FIRST NAME: ID:
TODAYs DATE:
TIME OF YOUR LECTURE ON MWF: ; TAs NAME:
Instructions
(1) YOU MUST WRITE YOUR ANSWERS
13.2.25
From last day: Covariance
between two random variables.
The multinomial distribution.
New: Joint continuous densities
(I)
Feb 24th
Juana Sanchez
Stat 100/Sanchez-Intro Probability
UCLA Dept of Statistics
1
Announcements
Homework 6 due Wednesda
Notes
Independent Events
Juana Sanchez
jsanchez@stat.ucla.edu
UCLA Department of Statistics
January 23, 2013
J. Sanchez
Stat 100A. Conditional Probability
Announcements
Notes
Homework 2 is due Today at the beginning of lecture. Homework
turned in at the e
Stat 100 -Intro Probability
Homework 6 Key
J. Sanchez
UCLA Department of Statistics
Instructions
(1) No late homework accepted under any circumstances.
(2) Must hand in in person to prof. Sanchez at the beginning of lecture. Homework turned in at the end
Notes
Conditional Probability
Juana Sanchez
jsanchez@stat.ucla.edu
UCLA Department of Statistics
January 18, 2013
J. Sanchez
Stat 100A. Conditional Probability
Announcements
Notes
Homework 2 is due on January 23rd.
Homework 1 key was posted (see homework
Notes
Continuous Random Variables: The Gamma
Density,Uniform density, Density of functions of a
random variable
Juana Sanchez
jsanchez@stat.ucla.edu
UCLA Department of Statistics
Feb 11, 2013
J. Sanchez
Continuous Random Variables
Announcements
Notes
Home
Stat 100 -Intro Probability
Homework 7
J. Sanchez
UCLA Department of Statistics
Instructions
(1) No late homework accepted under any circumstances.
(2) Must hand in in person to prof. Sanchez at the beginning of lecture. Homework turned in at the end of l
Notes
Random variables
Continuous random variables
Juana Sanchez
jsanchez@stat.ucla.edu
UCLA Department of Statistics
February 8, 2013
J. Sanchez
Random Variables-Continuous
Announcements
Notes
Practice project is posted and due on Wednesday, Feb 13th. It
Notes
Application of Independence to Genetics. Risk and
Odds.
Juana Sanchez
jsanchez@stat.ucla.edu
UCLA Department of Statistics
January 26, 2013
J. Sanchez
Stat 100A. Conditional Probability
Announcements
Notes
Homework 3 is due on Wednesday, January 30t
13.2.25
Jointly Distributed Discrete
Random Variables
Two variable case
February 2013
Stat 100/Sanchez-Intro Probability
1
Announcements
Homework 6 due Wednesday, Feb. 27th,
beginning of lecture.
February 2013
Stat 100/Sanchez-Intro Probability
2
Today
Announcements
Homework 1 due on Wednesday, Jan 16th at the !
beginning of class. Homework turned in later !
will lose points. !
TA session room has changed. Starting this week, !
go to Boelter 2444!
The syllabus has been updated. Remember that it is !
Notes
Random variables
Discrete Random Variables
Juana Sanchez
jsanchez@stat.ucla.edu
UCLA Department of Statistics
January 28, 2013
J. Sanchez
Stat 100A Intro Probability
Announcements
Notes
Homework 3 is due on Wednesday, January 30th, beginning of
lect
Notes
Random variables
Discrete Random Variables III
Juana Sanchez
jsanchez@stat.ucla.edu
UCLA Department of Statistics
February 2, 2013
J. Sanchez
Stat 100A Intro Probability
Announcements
Notes
Homework 4 is due on Tuesday, at the end of the TA session.