CS112 Homework 7
Q1. Consider a birth-death system in which k = and k = k for k 0. For all k, nd
the dierential dierence equations for Pk (t) = P [k in system at time t].
Q2. Consider a taxi station w
CS112: Modeling Uncertainty in Information Systems
Homework 5
Due Friday, June 8, at the beginning of section
Please refer to the course academic integrity policy for collaboration rules. In particula
CS112 HOMEWORK 3
1. An articial intelligent robot is detecting an item placed in front of him using a newly
invented computer vision algorithm. After calculating, he thinks that the item has 35%
proba
CS112 HOMEWORK 1
1. Find the Laplace Transform of:
(1) f (x) = eax
(2) f (x) = x2
(3) f (x) = 4x2 3x + 7
(4) f (x) = (x 1)2
2. Sum the series:
n
3
i=1 i
3. Answer the following questions:
(1) There ar
CS112 HOMEWORK 4
1. A given program has an execution time T that is uniformly distributed between 10 and 20
seconds. The number of interrupts that occur during execution is a Poisson random variable
w
CS112 HOMEWORK 1
1. Combinatorics
(1) For years, telephone area codes in the United States and Canada consisted of a
sequence of three digits. The first digit was an integer between 2 and 9, the secon
CS112 DISCUSSION 2
1. Probability Basic
(1) Let E, F, G be three events. Find expressions for the events that of E, F, G
(i) only E occurs
E (F G)c
(ii) both E and F but not G occur
E F Gc
(iii) at le
CS112 Homework 6
1. Consider a birth-death process with 4 states, where the transition rate from state 2 to state 1
is q21 = , and q23 = . Show that the mean time spent in state 2 is 1/( + ).
Solution
CS112 HOMEWORK 2
1. Express each of the following events in terms of the events A, B and C as well as the
operations of complementation, union and intersection:
(a) at least one of the events A, B, C
CS112 DISCUSSION 1
1. Elementary Math
(1) If a1 = 1 , an+1 = an +
2
an+1 an =
1
n
an an1 =
1
n1
what is an ?
1
n+1
1
n
1
n2
an1 an2 =
1
,
n2 +n
1
n1
1
3
a2 a 1 = 1
1
2
a3 a 2 =
1
2
1
So: an a1 = 1 n
CS112 DISCUSSION 4
1. Uniform Distribution
The amount of time, in minutes, that a person must wait for a bus is uniformly distributed
between 0 and 15 minutes, inclusive.
(a) What is the probability t
Discussion 5
1
Review
1.1
Expections
For a discrete random variable X with pmf pX (x),
E[X] =
xpX (x)
x
For a continuous random variable X with pdf f (x),
xf (x)dx = X
E[X] =
Binomial distribution: N
CS 112: Computer System
Modeling Fundamentals
Prof. Jenn Wortman Vaughan
March 31, 2011
Lecture 2
Reminders & Announcements
Pick up a copy of the course textbook
Take a look at the course website
(e
CS 112: Computer System
Modeling Fundamentals
Prof. Jenn Wortman Vaughan
April 5, 2011
Lecture 3
Reminders & Announcements
Pick up a copy of the course textbook
Homework 1 is due one week from today
CS 112: Computer System
Modeling Fundamentals
Prof. Jenn Wortman Vaughan
April 19, 2011
Lecture 7
Reminders & Announcements
Check your grade for homework 1 on Gradebook
Homework 2 is due on Tuesday,
CS 112: Computer System
Modeling Fundamentals
Prof. Jenn Wortman Vaughan
April 7, 2011
Lecture 4
Quiz #1!
Reminders & Announcements
Homework 1 is due in class on Tuesday
There was initially a small
CS 112: Computer System
Modeling Fundamentals
Prof. Jenn Wortman Vaughan
April 12, 2011
Lecture 5
Reminders & Announcements
Quiz grades are posted on Gradebook
Homework 2 will be posted on the cours
CS 112: Computer System
Modeling Fundamentals
Prof. Jenn Wortman Vaughan
March 29, 2011
Reasoning About Uncertainty
CS 112: Computer System
Modeling Fundamentals
Prof. Jenn Wortman Vaughan
March 29, 2
CS 112: Computer System
Modeling Fundamentals
Prof. Jenn Wortman Vaughan
May 5, 2011
Lecture 11
Reminders & Announcements
Homework 2 grades have been posted in Gradebook
Homework 3 is due this Tuesd
CS 112: Computer System
Modeling Fundamentals
Prof. Jenn Wortman Vaughan
April 26, 2011
Lecture 9
Reminders & Announcements
The course midterm is one week from today in class
The exam will cover all
CS 112: Computer System
Modeling Fundamentals
Prof. Jenn Wortman Vaughan
April 14, 2011
Lecture 6
Reminders & Announcements
Homework 2 has been posted on the website and is due
on Tuesday, April 26
Homework 5
CS 112: Modeling Uncertainty in Information Systems
Due to Friday Feb 27th , 2017 5:00 PM
Expectation and Variance
Problem 1. A given program has an execution time that is uniformly distrib
Homework 8
CS 112: Modeling Uncertainty in Information Systems
Due to Monday Mar 20th , 2017 5:00 PM
Problem 1. Consider a simple M/M/1 queueing system that models service of job in a
system. The jobs