EL630: Homework 3
1. (Book:3-1) Let p represent the probability of an event A. What is the probability that (a) A
occurs at least twice in n independent trials; (b) A occurs at least thrice in n independent
trials?
2. (Book:3-2) A pair of dice is rolled 5
EL630: Homework 4
1.
(Book: 4-9) Find f ( x) if F ( x) = (1 e x )u( x c).
F ( x)
c
x
(Hint: For any function h( x), we have h( x) ( x a) = h(a) ( x a), which is called the
sampling property of the impulse function.)
2. (Book: 4-10) If
X
is N (0, 4) find (
EL630: Homework 2
1. (Book:2-8) If A B, P( A) = 1/ 4, and P( B) = 1/ 3, find P( A | B) and P ( B | A).
2. (Book:2-9) Show that P( AB | C ) = P( A | BC ) P( B | C )
and P ( ABC ) = P( A | BC ) P ( B | C ) P(C ).
3. (Book:2-12) A call occurs at time t , whe
1. In connectionless switching, the order of packets is always maintained. In other words, if packet A is sent out earlier than packet B, it will arrive at the destination earlier than packet B as well. A. True B. False 2. When a packet arrives at a route
1. What do multiple access protocols do? A. Allow a host to access multiple channels B. Allow multiple hosts to access the same media 2. A channel is shared by two stations A and B. At time t=0, A and B have frames to send simultaneously. Consider Non-Per
1. Flow control is used to adjust the sender's sending rate to the receiver's p rocessing speed. A. True B. False 2. Both stop-and-wait and sliding-window are based on feed-back loop control. A. True B. False 3. By properly tuning the system, stop-and-wai
1. A. B. C.
Traffic control can increase efficiency avoid congestion reduce average delay D. all of above 2. Without proper traffic control, a greedy user may get much more bandwidth than a normal user, which is unfair. A. True B. False 3. Which of the fo
1. A. B. 2.
TCP belongs to network layer. True False TCP must be implemented in each IP router. A. True B. False 3. TCP ports can be used to distinguish packets to different applications running on the same computer. A. True B. False 4. UDP has error-retr
1. You receive an email saying that your bank account has been suspended, you want to verify if this is really from your bank. This is related to A. Confidentiality B. integrity C. availability D. authenticity 2. You send a message to your friend, and you
Lecture 4
Chapter 4 The Concept of a Random Variable
4.1 Introduction
Example
In the fair-die experiment, if we assign to the six outcomes fi the numbers
X ( f i ) = 10i,
then, X( ) is a random variable.
i.e. X( f1) = 10, . X( f 6 ) = 60,
Definition
A ran
Lecture 3
Independence of Three Events
Definition
A1 , A2 , A3
and
are called independent if they are independent in pairs:
P ( Ai A j ) = P ( Ai ) P ( A j )
i j
P ( A1 A2 A3 ) = P ( A1 ) P ( A2 ) P ( A3 )
Note
Three events might be independent in pairs b
Lecture 2
Axiomatic Definition of an Experiment
An experiment is specified in terms of the following concepts:
1.
The set S of all experimental outcomes.
2.
The Borel field of all events of S.
3. The probabilities of these events.
The letter S will be use
EL630 Probability
Acknowledgments
First, I wish to thank Professor Unnikrishna Pillai. He recommended me to
Professor Henry Bertoni to develop this on-line course. For this course we will
use the book "Probability, Random Variables and Stochastic Processe
1. A voice channel needs 4kHz. Using FDM, how many voice channels can be supported with 128 kHz? A. Up to 16 B. Up to 32 C. Up to 8 D. Up to 64 2. Suppose signal A and signal B are multiplexed using FDM, they are overlapped in the time domain. A. True B.
1. B 2. A 3. B 4. A 5. A 6. B 7. sampling:frequencyistwiceofthehighestsignalfrequency:2x4kHz=8kHz quantization:256levelsmeansthenumberofbitseachsampleneedsis log2(256)=8bitsthebitrateofeachvoiceis:8kHz*8bits=64kb/sthereare 32suchsignals,sotheansweris32*64
1.
FM radio is based on duplex transmission. A. True B. False
2. 3.
How is multi-mode fiber different from single-mode fiber? When performing lossless sampling of an analog signal, lowest sampling rate is 2B, what does the B stand for? A. Frequency band o