Stat 3320 Homework 3
1. The lifetime, in years, of some electric component is a continuous random variable with density
_ K/rc4 for :0 2 1 years
ﬁx) _ { 0 otherwise
a)- I %0lx=kaX#Ax=k(‘%>X-BIT
baa—w
'3‘ (50V P
—%=1 S>ll<i3l
we, "Ml?
relay—I] 2. The ar

Outline
Total Probability
Bayes Rule
Lecture 6. Independence and Conditional
Probability
YULIA R. GEL
CS/SE/STAT 3341 Probability and Statistics
in Computer Science and Software Engineering
January 31, 2017
Outline
Total Probability
Bayes Rule
1
Total Pro

Outline
Definition of probability
Axioms of Probability
Examples
Probability of a Sum
Lecture 3. Basic Probability Rules
YULIA R. GEL
CS/SE/STAT 3341 Probability and Statistics
in Computer Science and Software Engineering
January 19, 2017
Outline
Definiti

Outline
Distribution Functions of a Random variable
Types of Random Variables
Expectation and Variance of a Discrete Random Variable
Lectures 7. Random variables and random vectors.
Joint and marginal distributions. Expectation and
variance.
YULIA R. GEL

Outline
Operations of set theory
Lecture 2. Basic Probability Rules
YULIA R. GEL
CS/SE/STAT 3341 Probability and Statistics
in Computer Science and Software Engineering
January 17, 2017
Outline
Operations of set theory
1
Operations of set theory
Outline
O

PH1831 Homework #6
Weilu Han
Klein and Moeschberger
Chapter 8
Exercise 8.2,
a)
let z1 = 1 is subject is in treatment group, 0 otherwise.
let z2 =1
is subject is in control group, 0 otherwise.
b)
let z1 = 1 is subject is in treatment group, 0 otherwise.
le

PH1831 Class Exercises Lecture 2
. set obs 1
obs was 0, now 1
. gen mean = 1/.001
. gen median = ln(2)/.001
. gen survival = exp(-.001*2000)
. su
Variable |
Obs
Mean
Std. Dev.
Min
Max
-+-mean |
1
1000
.
1000
1000
median |
1
693.1472
.
693.1472
693.1472
su

PH1950
Homework 1
1.
It is assumed that the systolic blood pressure (SBP) and diastolic blood pressure (DBP) follow a bivariate
normal distribution with parameters ( 1 , 2 , 12 , 22 , )T , where
1 represents the mean of the SBP,
2 represents the mean of

Stochastic Process Homework 3
1. The infinitesimal matrix is constructed as follows:
[
]
Since the sojourn time is exponentially distributed:
T ~ Exp(
P ( X ( t+ t )=0| X ( t ) =0
P(T t)
1 t +o( t)
P ( X ( t+ t )=1| X ( t )=0
P(T t)
t+ o( t )
P

Exercises
3.2
1. we set the prior
j=1,
j=1,2 ;
( 1 , 2 , 3 ) y Dirichlet (295, 308,39)
( 1 2 , 22 , 32 ) y
Dirichlet (2 89 , 333 , 20 )
2. the resulting posterior distribution for
'
js
is dirichlet with parameters
j+ y j
3. we simulate with the followin

2.2
(a) We first write down the survival equation:
S ( x)=e ( x )
P(a rat will be tumor free at 30 days) :
(
2
)
S ( 30 )=e 0.001 30 =0.407
P(a rat will be tumor free at 45 days) :
2
S ( 45 )=e(0.001 45 )=0.132
P(a rat will be tumor free at 60 days) :
2
S

Lecture 0
Introduction to Stochastic Processes
Examples of Discrete/Continuous Time Markov Chains
In this lecture, we begin to introduce some notions of stochastic processes and to present some terminology
commonly used in stochastic processes. We first f

Outline
Independence and Conditional Probability
History Excurse with Pascal
Lecture 4 and 5. Independence and Conditional
Probability
YULIA R. GEL
CS/SE/STAT 3341 Probability and Statistics
in Computer Science and Software Engineering
January 24 and 26,

PROBABILITY AND STATISTICS
FOR COMPUTER SCIENTISTS
SECOND EDITION
K13525_FM.indd 1
7/2/13 3:37 PM
K13525_FM.indd 2
7/2/13 3:37 PM
PROBABILITY AND STATISTICS
FOR COMPUTER SCIENTISTS
SECOND EDITION
Michael Baron
University of Texas at Dallas
Richardson, USA

CS/SE/STAT 3341 Section 002
Spring 2017
Probability and Statistics in Computer Science and Software Engineering
Instructor:
Yulia R. Gel
Lectures:
TuTh 100 2.15 pm
Office:
GR 3.420
Phone:
(972) UTD-6447
ll
E-mail:
[email protected]
Office hours:
Tue 425 52

1. Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the
actual air pressure in each tire is a random variableX for the right tire and Y for the left tire, with joint pdf
a. What is the value of K?
b

Problems Solving in Class for Chapter 2 for Stat 3320
1. Suppose a computer code has no errors with probability 0.45. What is the probability
that the computer has at least one error?
2. There is a 1% probability for a hard drive to crash. Therefore, it h

Chapter 3 Discrete Random Variables and Their Probability Distributions
A random variable is a function of an outcome,
X = f (! )
In other words, it is a quantity that depends on chance.
The domain of a random variable is the sample space S.
Denition: Col

OPMT 600 Statistical Methods for Decision Making Fall 2016
Assignment #4 Discrete and Binomial Probability
Due Oct. 4th
You will need to use Minitab for portions of this assignment. Use Minitab to produce appropriate probabilities,
charts and graphs. Use

Part 1: Summarize and analyze your chosen study, article, or video:
Women have been ubiquitous in the workplace since in 1974. However, women still only make
up 30% of the technical workforce, with far fewer numbers among management teams, and
startup fou

OPMT 600 Statistical Methods for Decision Making
Assignment #2 Data collection and description
Due Sept. 20th
1. Complete the following problems from the textbook:
a. Problem 4.74
Investment
Mean
Return
Standard Deviation
Coefficient of Variation
Venture

OPMT 600 Statistical Methods for Decision Making Fall 2016
Assignment #3 Examining data and probabilities
Due September 27th
Note: You will need to use Minitab for this assignment. Type your answers or comments on this form.
According to a 2010 study publ

OPMT 600 Statistical Methods for Decision Making Fall
2016
Assignment #5 Continuous Probability and Sampling distributions
Due October 11
Note: Do your own tabulations (without Minitab) for this assignment when noted. All other
computations should be done

Homework 2
Problem of the week. Suppose a box contains 3 white balls and 3 black balls. The white balls
are labeled with 1, 2 and 3 respectively, and the same is true for the black balls. Suppose that a ball
is drawn randomly and it is noted that it is wh

Homework 1
Problem of the week. A computer hacker launches three independent virus attacks on a server.
The first attack is successful with probability 10%, whereas each of the second and the third attacks
is successful with probability 20%. Find the prob

Homework 3
Problem of the week. Suppose the number of network blackouts in a day has the following
probability distribution:
p(0) = 0.20, p(1) = 0.30, p(2) = 0.50.
Assume that the number of blackouts on different days are independent. What is the probabil

Outline
Motivation
Course Goals
Basic Probability Concepts (Chapter 2 MB)
Lecture 1. Introduction and
Basic Probability Concepts
YULIA R. GEL
CS/SE/STAT 3341 Probability and Statistics
in Computer Science and Software Engineering
January 12, 2017
Outline

3.6
I already answered part of 3.6 in the whole submission. But I need to change my plot of N, and theta
As the to answer why we need to change . I think from the model perspective, The N is unobserved
thus the hierarchal model better reflect the change o