CS112 Homework 7 Solution
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].
Solution:
dPi
= f lowIn f lowOut at each node i of the transition diagram.
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
with parameter t where T = t is the program execution ti
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 where taxis and customers arrive in a poisson process wi
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 particular, be sure to include
a list of anyone with whom you ha
Homework 5 Solution
Problem 1.
(a) E[N |T = t] = t, since for xed running time, the number of interrupts is a Poisson random
variable with mean t
(b)
20
E[N |T = t]fT (t)dt
E[N ] =
10
20
t
E[N ] =
10
1
dt
10
1
= |20 = 15
20 10
Problem 2. The required time
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%
probability to be an object A, 15% probability to be an obje
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 are 6 balls with dierent colors and 3 dierent boxes. You
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 least one event occurs
EF G
(iv) at least two events occu
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 second
digit was either 0 or 1, and the third digit was any
Homework 5
1. A given program has an execution time that is uniformly distributed between 10 and 20
seconds. The number of interrupts that occur during execution is a Poisson random variable with
parameter t where t is the program execution time. The prob
CS112 HOMEWORK 3 SOLUTIONS
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%
probability to be an object A, 15% probability to
CS112 Homework 8 Solution
Q1. Consider a simple M/M/1 queueing system that models service of customers at a store
checkout line. The customers arrive at the checkout at rate customers per hour. There is
a single server capable of serving customers at the
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%
probability to be an object A, 15% probability to be an obje
CS112 - Homework #6 Solution
1. There are N machines where N is a large number. Each machine has one
of three possible states and changes states (independently) according to a
Markov Chain with transition probabilities
0.7 0.2 0.1
0.2 0.6 0.2
0.1 0.4 0.
CS 112 Homework # 4, Due Tuesday 10/29/2002, 12:00pm
(You must show your work to receive credit)
Problems
[1] Big Blue Busses arrive at Hilgard station at 15-minute intervals starting at 7:00am. That is,
they arrive at 7:00, 7:15, 7:30, and so on. If a st
Math 210
Distributing Balls into Boxes
The same combinatorial problem frequently can be phrased in many different ways, and one of the most common ways to
phrase combinatorial problems is in terms of distributing balls into boxes. For this reason, it is i
UCLA
Computer Science Department
CS 112
Fall 2002
Midterm Exam #1
1 Hour & 50 minutes, Closed Books and Notes
SOLUTION KEY
Name:-Student ID:-
Points
Problem 1
7
Problem 2
3
Problem 3
3
Problem 4
7
Total
Your score
20
October 21, 2002
1
Problem 1 (7 points
Midterm Exam #2
CS 112, Fall 2002
November 18, 2002
UCLA
1 Hour & 50 minutes, Closed Books and Notes
SOLUTION KEY
Name:-Student ID:-
Points
Problem 1
15
Problem 2
10
Problem 3
10
Problem 4
15
Total
Your score
50
Explain your work to receive credit
1
Probl
Networks II Worksheet Two
Richard G. Clegg,
richard@richardclegg.org
March 30, 2006
Birth Death Processes and Queuing
Question 1. Consider the M/M/m/m queue. That is an M/M/m queue where, if all servers
are busy then the customers are turned away. Model t
Recursive Estimation
Raaello DAndrea
Spring 2014
Problem Set 1:
Probability Review
Last updated: March 19, 2014
Notes:
Notation: Unless otherwise noted, x, y, and z denote random variables, fx (x) (or the short
hand f (x) denotes the probability density
CS112 Homework 2 Solution
1.
Note: (f) changed to:
2.
3.
(a)
(b)
(c)
4.
5. In order to have a path with operational components, serial components are all
required to be operational, whereas paralleled ones are required to have at least one of
them operati
CS112 HOMEWORK 4 SOLUTION
1. 1. The packets are sent from a server to a client host. The client host notices that the
time interval of two consecutive packets is uniformly distributed between 10ms to 20ms.
(1) Suppose one packet just arrived. What is the
CS112 Homework 8
Q1. Consider a simple M/M/1 queueing system that models service of customers at a store
checkout line. The customers arrive at the checkout at rate customers per hour. There is
a single server capable of serving customers at the rate of c
SOLUTION
CS112 HOMEWORK 2 FALL 2013
1. (a) A B C
(b) (A B C C C ) (AC B C C ) (AC B C C) (AC B C C C )
(c) (A B C)C
(d) A B C
(e) (A B C C C ) (AC B C C ) (AC B C C)
(f) A B C C
(g) A (AC B C )
2. P (A) = 21 , P (B) = 12 , P (C) =
P (A B) = 13 , P (A C) =
CS112 HOMEWORK 2 SOLUTION
(1) Express each of the following events in terms of the events A, B and C as well as the
operations of complement, union and intersection:
(a) at least one of the events A, B, C occurs
(b) at most one of the events A, B, C occur
Discussion 4
1
Expectation and Variance
1.1
Expections
1. For a discrete random variable X with pmf pX (x),
X
E[X] =
xpX (x)
x
For a continuous random variable X with pdf f (x),
Z
E[X] =
xf (x)dx = X
2. If Y = g(X),
Z
g(x)fX (x)dx
E[Y ] =
E[Y ] =
X
g(xi
Name:
Student ID:
CS 112 SAMPLE FINAL Winter 2016
Notes:
1: The final is closed book, closed notes.
2: Calculator allowed. No other electronic devices allowed.
3: One-page cheat sheet allowed.
Problem 1 (10 Points)
Problem 2 (6 Points)
Problem 3 (8 Points
CS112 - Homework 5 Solution
1. There are N machines where N is a large number. Each machine has one
of three possible states and changes states (independently) according to a
Markov Chain with transition probabilities
0.7 0.2 0.1
0.2 0.6 0.2
0.1 0.4 0.5
Name:
Student ID:
CS 112 SAMPLE FINAL Spring 2016
Notes:
1: The final is closed book, closed notes.
2: Calculator allowed. No other electronic devices allowed.
3: One-page cheat sheet allowed.
Problem 1 (10 Points)
Problem 2 (6 Points)
Problem 3 (8 Points
Name:
Student ID:
CS 112 SAMPLE FINAL Spring 2016
Notes:
1: The final is closed book, closed notes.
2: Calculator allowed. No other electronic devices allowed.
3: One-page cheat sheet allowed.
Problem 1 (10 Points)
Problem 2 (6 Points)
Problem 3 (8 Points