ELEC210 Spring 2011 Homework4Solution
1. The random variable X has cdf as shown in the figure below:
(a) What type of random variable is X?
(b) Find the following probabilities:
,
,
,
,
,
.
Solution(16):
(a) (4)The cdf is neither continuous nor piecewi
ELEC210 Spring 2011 Homework4
1. The random variable X has cdf as shown in the figure below:
(a) What type of random variable is X?
(b) Find the following probabilities:
,
,
,
,
,
.
2. A point is selected at random inside a square defined by
.
Assume the
ELEC 308 Engineering Optics
FINAL EXAMINATION
DATE:
May 31, 2007
TIME:
4:30 pm  7:30 pm
PLEDGE OF HONOR
On my honor as a student of Hong Kong University of Science and
Technology, I have neither received aid from others nor given aid to
others while taki
Assignment 3 (part 2)
March 26, 2010
1. The figure below shows a twolens system and an object. Diagrammatically locate (i)
aperture stop and appropriate pupils, (ii) field stop and appropriate windows, (iii) the
image (using marginal and chief rays).
L1
Assignment 3
Due date: March 16
1. Problem 6.20 and 6.23.
2. Analyze a Tessar lens using matrix method (Figure 6.10 on page 251)
3. (i) Design an achromatic doublet with 45 mm focal length. (ii) Find principal and
focal planes of the doublet using matrix
Assignment 2
Due date: March 8, 2010
1. Problem 6.2 (NOTE: you do not need to calculate the position of the field stop).
2. Problem 6.5 and 6.9 on page 278.
3. Problem 5.42, p.237. Solve the problem using (a) graphical ray tracing, (b) matrix
method.
4.
P
Assignment 1
Due date: Feb. 26
1. Problems 4.6 and 4.8 on page 142.
2. Problems 4.12, 4.17, 4.23 and 4.25 on page 143.
3. Problem 5.8, 5.10 and 5.12 on 235.
4. Problems 5.29 and 5.30 on page 236.
5. (i) Design a costeffective lens of 60 mm focal length a
1)
a)
Solution1:
.
InTCPchannel,
We have RTT
4
400ms,
Buffersizeweneed:w
M
.
2.13Mbit
.
Or
Solution2:
InTCPchannel,
We have RTT
4
400ms,
Buffersizeweneed:w
4Mbps
400ms
1.6Mbit
(Whetherornottohave0.75intheexpressiondependsonhowyoumodeltheTCPchannel,
here,w
1. Two users, Alice and Bob, use public keys to communicate. The two public keys are:
Pa+: Alice public key (n, d)=(33,7)
Pa: Alice private key (n, e)=(33,3)
Pb+: Bobs public key (33, 13)
Pb: Bobs private key (33, 17)
Assume each of the 26 letters is re
ELEC315HW6SOLUTION
1
a)
/
600bits
5Mbps
5
10 s
1.2
10
1
5
e
1
b)
82.75%
2
M
e
1
s
1
5
10 s
44.44%
2
a) Becausethenumberofstationsatbothsidesofthebridgeisequal,theprobabilityofa
transmissiontopassthebridgeis0.5.Thetotalcapacityisgivenby:
2 10M
13.33Mbps
Homework Assignment 7
ELEC315
Q1. A CSMA/CD cable LAN has the following parameters:
Channel capacity: 5 Mbps
Cable length: 1 Km
Signal speed: 2x10^8 m/sec
Packet length: 600 bits
(a) Use the formula given in the class notes, compute the maximum efficiency
(1) Consider a pure (unslotted) ALOHA channel with the following
characteristics:
Capacity: 2 Mbps
Packet length (fixed): 1000 bits
Suppose that the probability that a station has a packet to transmit in one packet
length is 0.02 and 50 stations are shar
HW 5 Reference Solution
Q1. Solution:
a) The initial routing tables of 5 nodes are listed as follows:
For Node A
Destination Distance Next_Hop
A
0
B
1
B
C
4
C
D
E
For Node B
Destination
A
B
C
D
E
Distance
1
0
3

Next_Hop
A
D

For Node C
Destination
1)
Routers in the following network use distance vector routing. When the system is
first powered up, a routers routing table only contains the distance estimates to its
neighbors. The distances to nonneighbors are set to infinity. To simplify the
discus
(1) DNS is a mapping between IP addresses and domain names. Is this mapping one to
one? (b) Is www.ust.hk an alias or a canonical name? (c) What command we can use to
find the 13 root DNS servers ip addresses?
(2) This question explores URL hashing for co
1
(a)Not necessarily. Sometimes one DNS can map to several IP address.
(b)A canonical name.
(c)To find the 13 root DNS serverss IP address, we could use the command:
nslookup type=ns .
2
(a)www.umass.edu: 23+23+23+21+13+1+19+19+5+4+21(modulo 3)=1;
www.eu
1TherateatwhichTCPsendsdataisafunctionofthecongestionwindowandthecurrentRTT.
WhenthewindowsizeiswbytesandthecurrentroundtriptimeisRTTseconds,thenTCPs
transmissionrateisroughly
RTT
.
500 bytes,aslongas
SoduringtheithRTT,wesentW
W
WehaveW
10, W
500kbps
So
1
(1) MTU = 500 Bytes. RTT = 250 ms. Assume the sender will grows its window
linearly according to the following formula: Wi= Wi1 + 10 and W0 = 1. When a
packet is dropped, the window size will be reduced to W0 and starts all over again.
Assume the network
(1)
a. For the queuing delay, you should try Ping many times at some idle time of one day. The
minimum roundtrip time obtained can be considered as the RTT without queuing delay.
For the processing delay, one packet processing task is only 1ms in one rou
(1) The following is the result of the ping command: ping www.yahoo.com, which
was executed around 4pm. The source machine is eez176.ee.ust.hk, which is
located in Hong Kong. Assume the destination machine is located in San Jose in
California.
Pinging www
1)
a) Suppose the number of sharing stations is N, the probability that a station has a
packet to transmit in one packet time is p. A transmission is successful only when
there is one station transmits at the current slot and no more station will transmit
(1)
(a) M = help = 01000 00101 01100 10000
G = 101011
M * 25 mod G = R = 10010 = 18(10)
So the digital signature = PA(R) = 183 mod 33 = 24 = 11000(2)
(b)
message
h
e
l
p
PA(R)
numeric representation
01000=8
00101=5
01100=12
10000=16
011000=24
PB+(M) = c
ELEC151 Digital Circuits and Systems
Lecture Note #9 Rapid Prototyping
ELEC151 Digital Circuits and Systems
The Elements of Modern Design
Representations, Circuit Technologies, Rapid Prototyping
Finitestate Machine Implementation
by standard logic (TTL
ELEC151 Digital Circuits and Systems
Lecture Note #8 Finite State Machine
ELEC151 Digital Circuits and Systems
Finite State Machine and Sequential Logic
Analysis of sequential circuit
54
Mealy and Moore machine
Reverse engineering
From schematics to
ELEC151 Digital Circuits and Systems
Lecture Note #7 Hardware Description Language
Hardware Description Language
39
Design entry for logic simulation and synthesis
Two IEEE standards, and many others
VHDL used in PLD, (originated by DoD, more popular
ELEC151 Digital Circuits and Systems
Lecture Note #6 Registers and Counters
Registers
ELEC151 Digital Circuits and Systems
TTL Functional Selection P.13
61
A group of flipflops in parallel
Shift Registers
62
A group of flipflop in series
Counter
ELEC151 Digital Circuits and Systems
Lecture Note #5 Sequential Logic
ELEC151 Digital Circuits and Systems
Combinational vs Sequential Logic
Sequential circuits
51
Combinational Logic
feedback and clock
Latches
Outputs are solely determined by input
ELEC151 Digital Circuits and Systems
Lecture Note #4 Combinational Logic
Combinational vs Sequential Logic
Combinational circuits
Combinational Logic
Design procedure and analysis skill
41, 42, 43
Circuit examples
ELEC151 Digital Circuits and Syste
ELEC151 Digital Circuits and Systems
ELEC151 Digital Circuits and Systems
Lecture Note #3 GateLevel Minimization
Logic Minimization
Karnaugh map or Kmap
Design Sequence:
31, 32, 33
1. Truth Table (input and output relations)
Derive truth table fr
ELEC151 Digital Circuits and Systems
Lecture Note #2 Boolean Algebra
ELEC151 Digital Circuits and Systems
Boolean Algebra/Logic Circuits
Basic definitions and axioms
Laws and theorems of Boolean algebra
21, 22
23, 24
Boolean Algebra
25
Digital Ci