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CS607 Artificial Intelligence Assignment No 4 Spring solution 2012

Mr. Yousaf Ali Khan, Mr. Hamza and Mr. Khurram own an aero-plane engine manufacturing
factory in Texila, Pakistan. They have been developing spare parts and complete aero-plane
engines. They have decided to develop Fault Diagnosis System in case either they do not found
already developed computer expert system or not found to required number of human experts to
identify the faults in aero-plane engines or if Fault Diagnosis System is costly or not has full and
final documentation then new expert system must be developed.
In case of development of their own Fault Diagnosis Expert System, this system contains
the knowledge of many experts and provides permanent documentation of the decision process.
Even if this system provides the training of new human experts will be easy through the use of
this system. If this system will help in a way that production will be faster with less chance of
errors in the finished products and system can be available 24 hours a day 365 days a year. Then
all owner of the factory will be very happy and satisfied by that expert system.

Express the statements in the form of facts and rules using IF, THEN format and compound statements.

Solution:

Express the statements in the form of facts and rules (using IF, THEN format and compound statements).

Sim and Sam are sisters. They’ve decided that they will have a joint wedding party either if they do not find a better
day or they cannot afford separate weddings. In any case, once they decide to have a joint wedding party, they will plan
well and have fun. They will be happy if the party goes well and they both get pretty wedding rings.

Facts:
Sim and Sam are sisters

Rules:
IF they do not find a better day
OR If they cannot afford separate weddings
THEN they will have a joint wedding party

IF they decide to have a joint wedding party
THEN they will plan well
AND they will have fun

IF the party goes well
AND they both get pretty wedding rings
THEN they will be happy

CS401 Computer Architecture and Assembly Language Programmin GDB Solution Spring 2012

Presently, we are having 5th Generation of Programming Languages. The new programming languages are offering sophisticated tools, support and flexibility for better programming. However, we still interested in Assembly Language Programming. Find out the basic reasons and advantages, which still make Assembly Language Programming as one of important and basic tool

Solution:

Assembly language is very useful for routines that require high speed and highly optimized code. It is also required for Boot Loaders (i.e. LILO, GRUB, etc…) and Operating Systems.
Most high level languages are very slow in comparison to ASM as has already been stated but this is mainly due to the multiple levels of abstraction that separates native binary from the HL language in question.

High Level languages have HUGE runtime dependancies, ASM can be optimised to have none whatsoever which is why they are indeed used in bootstrapping and OS installers, it lets you run a program on a completely blank computer.

The other benefits of knowing ASM include gaining a much deeper understanding of how a computer works at the lowest level. Thi definitely affects the way you write code in HLL too.
if you know assembly language, stick with it, it is THE BEST, the compiler does not mess with your code, it does not change any of the ASM code, it simply directly, converts each instruction to machine code, and thats it. It wont check for extensive errros like VB or others, such as ‘runtime error file not found’ – none of that because the compiler has not messed with your code.

Other advantages…
The programmer has COMPLETE control over how the program works, unlike other high level languages.

Final advantage, filezise – a program which only displays a messagbox then quits (including the windows DLLs)

ASM: 3kb
VB6: 16kb

^thats a huge difference
Assembly Language is the closest abstract to machine code. In many cases, you might have a processor directive say 0010101001010101010111111111000111, in assembly – instead of remembering all those 1, an 0′s you might have to remember MOV es,ax

(I have no idea, btw, what that binary sequence means!)

You then use an assembler to convert your instructions into machine code – with no interference or optimisation done by the assembler.
Assembler is still a high level programming language and is the next step up in making code easier to understand or human readable, it is still converted to machine language in order for the computer to understand it which is the lowest level.

It’s quicker to develop applications using the latest higher level language tools and the differences in performance these days is hard to notice as most machines tote enough power it doesn’t make much of a real difference.

But in terms of speed, effeciency, can easily create your own programming language and re-invent the wheel, and portability assembler stands out a bit.

The downside is there’s alot missing in terms of all the latest tools and features for using syntax for simplicity and rapid application development.

The programs are small, lightweight, and don’t require bulky runtimes which need to be downloaded, plus you develop totally for free.

Size and speed isn’t so much an issue as time, money, and ease of development these days, plus, people aren’t as deeply educated and focus is only on working with the IDE more so than how the internal code itself works, this develops false positives and leaves many security exploit possibilities open in the higher level languages.

A big comparison would be this, let’s say you needed an application with moderate to complicated functionality complete for commercial business application for a client, you aren’t well skilled in assembler but could popup something in short amount of time in higher level language, if it takes a few to several years to complete in assembler and you only have a few days to a week your best bet is higher level language to get it done now and get paid.

Either way, it’s all about picking the language that you’re comfortable working with and can understand, don’t be afraid to try something new and keep developing!

3^rdQuiz(CS507)Please Correct me, if you find any mistake.lushahz@gmail.com

Both software objects and real time objects have ________

Identity and behavior
Identity and state
Identity, state and behavior
State and behavior

The flowchart helps in locating and correcting errors.

True
False

Which of the following is not same as key performance indicator or KPI.

CSF
PIN
Both options a and b
None of them

______________ time is saved through an error free designed system.

Deployment
Development
Configuration
Testing

A category of objects _______ the same attributes, operations and relationships.

Inherit (doubted)
Share
Collaborate
Use

__________ factor is not considered during OO Design.

Encapsulation
Usability
Information hiding (doubted)
Confidentiality

Which of the following carry characteristics of specialization?

Sub classes
Sub Interfaces
Sub objects
super set

Operations are usually called via ______

Methods
Functions
Signatures
Interfaces

Both software objects and real time objects have__________

Identity and behavior
Identity and state
State and behavior
Attribute and property

Process indicates:

Procedure
Flow
Activity
Result

Create table instructor syntax:

Create table INSTUCTOR(INSTUCTOR_ID char(50),FISRT_NAME char(50),LAST_NAME)

Char(50),LAST_DEGREE char(50),SALARY char(50),CITY char(50), HIRE_DATE detetime);

Insert into INSTRUCTOR:

Insert into INSTRUCTOR values(‘50’,‘AHMAD’,‘ALEEM’,‘MS’,‘40000’,‘ISLD’,’15-JAN-2011’);

Insert into INSTRUCTOR values(‘55’,‘MUHMMAD’,‘HASAN’,‘MS’,‘42000’,‘ISLD’,’16-FEB-2010’);

Insert into INSTRUCTOR values(‘60’,‘TALHA’,‘ALI’,‘phd’,‘80000’,‘LHR’,’18-JUN-2008’);

Insert into INSTRUCTOR values(‘70’,‘HANNAN’,‘NAWAZ’,‘phd’,‘76000’,‘LHR’,’20-DEC-2008’);

Insert into INSTRUCTOR values(‘80’,‘WAJID’,‘ALI’,‘MS’,‘45000’,‘LHR’,’09-AUG-2008’);

Insert into INSTRUCTOR values(‘85’,‘ASIF’,‘AHMAD’,‘MIT’,‘50000’,‘MUL’,’19-MAY-2010’);

Insert into INSTRUCTOR values(‘90’,‘TAHIR’,‘MOHSIN’,‘MCS’,‘38000’,‘MUL’,’27-FEB-2009’);

Insert into INSTRUCTOR values(‘95’,‘BAKIR’,‘NAWAZ’,‘MS’,‘40000’,‘ISLD’,’12-AUG-2011’);

Insert into INSTRUCTOR values(‘100’,‘FAHAD’,‘AHMAD’,‘Phd’,‘90000’,‘ISLD’,’07-APR-2008’);

Create table student syntax:

Create table STUDENT (STUDENT_ID char(50),STU_NAME char(50),SEMESTER char(50),SPECILIZATION char(50).INSTRUCTOR_ID char(50));

Insert into student syntax:

Insert into STUDENT values(‘1’,‘AHMAD’,‘2’,‘NETWORKS’,‘50’);

Insert into STUDENT values(‘2’,‘ASIM’,‘2’,‘NETWORKS’,‘55’);

Insert into STUDENT values(‘3’,‘SAJID’,‘3’,‘DATABASES’,‘60’);

Insert into STUDENT values(‘4’,‘SHUJA’,‘4’,‘AL’,‘70’);

Insert into STUDENT values(‘5’,‘ZEESHAN’,‘1’,‘DATABASES’,‘80’);

Insert into STUDENT values(‘6’,‘HASEEB’,‘2’,‘SOFTWARE ENGINEERING’,‘85’);

Insert into STUDENT values(‘7’,‘MUDASSAR’,‘3’,‘SOFTWARE ENGINEERING’,‘90’);

Insert into STUDENT values(‘8’,‘QASIM’,‘3’,‘DATABASES’,‘95’);

Insert into STUDENT values(‘9’,‘Fahad’,‘4’,‘NETWORKS’,‘100’);

Select Query syntax:

Select STUDENT.STUDENT_ID, INSTRUCTOR.LAST_NAME, INSTRUCTOR.LAST_DEGREE INSTRUCTOR.HIRE_DATE, INSTRUCTOR.INSTRUCTOR_ID, STUDENT.INSTRUCTOR_ID, STUDENT.STU_NAME FROM STUDENT INNER JOIN INSTRUCTOR ON STUDENT.INSTRUCTOR_ID = STUDENT.INSTRUCTOR_ID,

CS501 Assignment # 4 Idea Solution,,,,,

MIPS = Millions Instruction Per Second
Please do not for Hard Drive Case 500 instead of 250, cause in assignment hard drive speed is double 2MB/sec.
Please be aware that CPU instruction speed is not fully dependent on Perpherial Device speed, Bus speed and capacity is also occur significant roll in that senario.

For Hard Drive:

10^6 = 1 Million (10,00,000)
first calculate how many bits in 2MB = 16777216 (bits in 2 megabyte)
1048576 times data send in one second according to our bus speed 16-bit (16777216/16)

After that convert this data into Kilobyte and calculte Polled and get percentage.
But remember that our assignment senario is 100 MIPS so divide value is 100 MIPS.

Floopy Drive is also same calculation process follow, but replace accurate values.

If you have any problem feel free to contact me.
mc100204818@vu.edu.pk

CS502 Assignment # 4 Solution

Question:

Give an example of a directed graph G = (V, E), a source vertex s V, and a set of tree edges Eπ ⊆ E such that for each vertex v V, the unique path in the graph (V, Eπ) from s to v is a shortest path in G, yet the set of edges Eπ cannot be produced by running BFS on G, no matter how the vertices are ordered in each adjacency list.

Solution:

Let V={s,1,2,3,4}
E={( s,1) ( s,2) ( 1,3) ( 1,4) ( 2,3) ( 2,4)}
Last, let

= {( s,1) ( s,2) (1,4) ( 2,3)}

If vertex 1 precedes vertex 2 on the queue for BFS, then any search will produce tree edges ( 1,3) and ( 1,4); otherwise, the tree will have edges ( 2,3) and ( 2,4).
22.2-6. There are no professional wrestlers, and r pairs of wrestlers for which there are rivalries. Find an O(n+r)-time algorithm to see if the wrestlers can be divided into ‘ good guys’ , such as rivalry is between a good and bad guy.
This question is equivalent to the following:
Given a graph on an vertices with r edges, determine whether the vertices can be divided into two parts, G,B such that no edges connects two vertices in G or two vertices in B.
It is easy to see that if such a division on possible, then there cannot be any odd length cycle; conversely, if there is no odd length cycle, a BSF can be used to construct the subdivision, start a BSF with any vertex s; call it ‘good’; put all adjacent vertices on the queue, and call them ‘ bad’; whenever a good (resp. bad) vertex is at the head of the queue, label any new adjacent vertex in the opposite way and put it on the queue. If there is no odd length cycle, there will be no ambiguity as to the designation. Since BFS takes O(n+r) steps, we are done.

PHY301 GDB solution

The topic is:
“Differentiate between Drift & Diffusion current in semiconductor. Elaborate your answer with the help of daily life example”

Solution:
The difference between drift current and diffusion current?
Drift Current b/w Diffusion Current:
The difference between drift current and diffusion current is that drift current depends on the electric field applied: if there’s no electric field, there’s no drift current. Diffusion current occurs even though there isn’t an electric field applied to the semiconductor. It does not have E as one of its parameters. The constants it does depend on are Dp and Dn, and +q and -q, for holes and electrons respectively. data copied from vu solutions dot com The first constants are called the diffusion coefficients, a proportionality factor. We don’t worry too much about these because they are constants. We do worry about the gradient of the concentration of p and/or n, though. But, since we are talking about a one dimensional situation when we are solving for current densities, we only worry about the gradient (or derivative) with respect to the x-plane.

The other difference between drift current and diffusion current, is that the direction of the diffusion current depends on the change in the carrier concentrations, not the concentrations themselves. In the equation, the signs are reversed as we are used to seeing them. We usually assign a +q to holes and -q to electrons. In the case of diffusion current, they are reversed to be opposite of the derivative of the concentrations. This occurs because the carriers are diffusing from areas of high concentrations to areas of low concentrations.

For example, if the derivative of p with respect to x is positive, then the concentration of holes is growing as you move towards the +x direction. Diffusion current will be the opposite of that, the holes will be diffusing in the -x direction to where there’s a lower concentration of holes. If the derivative is negative, the opposite will occur. The concentration of holes is decreasing as you go from the -x to +x direction. (snow) Therefore, holes will diffuse to the +x direction where there’s a lower concentration of holes. This is why the negative sign is needed in the equation for the hole diffusion current.

The same goes for electrons, but in this case, the signs cancel for a positive derivative because the electrons, carrying -q, diffuse to the -x direction where there’s less electrons. The sign remains if the derivative is negative, because electrons will be diffusing to the +x direction carrying a -q charge. For these reasons it’s not included in the equation for the electron diffusion current.

PAK301 2nd assignment solution 18 june 2012

Q. What do you know about the Objectives Resolution? Describe its importance in the constitutional history of Pakistan.
Solution:
Objective Resolution
It was the first constitutional document in the history of the Islamic Repubic of Pakistan that proved to be the 'foundation' of the constitutional development. It contained those objectives on which the future constitution was to be based as stated by the founder of the nation, Quaid-e-Azam in February 1948 "The constitution of Pakistan will be democratic and based on the fundamental laws of Islam....Islam and its ideology has thought us the lesson of democracy." It provided parameters and sublime principles to the legislators. It was a framework that provided a mechanism to achieve goals for a better life of the people of pakistan. It was approved on March 12,1949. It was moved by Liaquat Ali Khan, the first Prime Minister of Pakistan. The constituent assembly debated this resolution in at least five sessons. They delliberated this in great details on all clauses and provisions. There were some spesific objectives or goals that would be acceptable to the people of the newly created state who had suffered a lot under the Hindu-dominated majority. That's why it was termed as Objective Resolution(OR).The resolution proclaimed that the future constitution of Pakistan would not be modeled entirely on a European pattern, but on the ideology and democratic faith of Islam.
The main features of Objective Resolution
Sovereignty:
1. Sovereignty over the entire universe belongs to Allah alone.
Sacred Trust:
2. The authority which He has delegated to the state of Pakistan through its people for being exercised within the limits prescribed by Him is a sacred trust.
3. Constitution will be framed for sovereign, independent state of Pakistan.
4. The state shall exercise its power through the representatives of the people.
5. Principles of Democracy, freedom, equality, tolerance and social justice as enunciated by Islam will be fully observed.
Islamic principle:
6. Muslims shall be enabled to organize their lives in accordance with the teachings and requirements of Islam as set out in the Quran and the Sunnah. Huamn rights:
7. Minorities to have freedom to freely profess and practice their religions and develop their cultures.
8. Provisions for safeguarding the legitimate interests of minorities, backward and depressed classes.
State sovereignty:
9. Pakistan shall be a Federation with autonomous units. State’s sovereignty and territorial integrity will be protected.
International norms:
10. People of Pakistan should prosper and attain their rightful place in the comity of nations and make contribution towards international peace and progress and happiness of humanity.

Importance of "OR"

The Objectives Resolution, which combines features of both Western and Islamic democracy, is one of the most important documents in the constitutional history of Pakistan. At the time it was passed, Liaquat Ali Khan called it "the most important occasion in the life of this country, next in importance only to the achievement of independence".
The Resolution declared the sovereignty of God as the distinctive political philosophy. In the first principle the declaration of BISMILLAH describe the sovereignty of Almighty Allah. The Western democracy gives the notion that sovereignty lies in the people but this Resolution is important having the concept of the sovereignty of God. It clarified that people would utilize powers gifted by God so they would have to work within the limits prescribed by Him.
This resolution is of fundamental importance in the history of constitutions making in Pakistan because from the first constitution of 1956 till the constitution of 1973 (present constitution) whatever constitution was framed it was based on this objective resolution. It contains those steps and principles which were to be taken for the fulfillment of the basic aim of the freedom struggle that is the establishment of an Islamic society in Pakistan. Hence, it is a significant document in the constitutional history of Pakistan.
The exercise of the powers is a sacred trust. Which means they can't voilate His command and principles which have to be followed at all times. Nobody, any leader or institution can claim that his power or authority belongs to him or her. It is a responsibility and an oblication and thus as an obligation it is a sacred trust.The representatives of the people of Pakistan will manage the affairs under the universal ideology of democracy, freedom, equality, tolerance, and social justice with the spirit of an Islamic framework. These principle are the foundation and bases of any civilized political system.The Resolution pledged to give the due respect and rights to the minorities, backward and depressed classes in the benign society of Pakistan. Their rights, interests, religion and culture were not confuted.
It’s important that the Resolution promised the federating units for due powers, autonomy and territorial integrity. The Objectives Resolution is a basic and primary document of the constitutional history of Pakistan. It is a framework that provides mechanism to achieve goals for a better life of the people of Pakistan. It’s important that it embraces centrality of Islam to polity sustaining their links with the pre-independence period. The AIML leaders were modernist Muslims not in favour of an orthodox religious state. Therefore, they selected the middle way abiding by the Islamic laws and the international democratic values.
The Resolution remained ‘Preamble of all the constitutions
due to its importance. The sovereignty belongs to Almighty Allah is incorporated in all the constitution of Pakistan.

Note:please change it in your own wording

Another Solution:

This resolution was passed by the First Constituent Assembly in March 1949 under leader ship of Liaquat Ali Khan. It contained those objectives on which the future constitution was to be based as stated by the founder of the nation, Quaid-e-Azam in February 1948, said:

"The constitution of Pakistan will be democratic and based on the fundamental laws of Islam....Islam and its ideology has thought us the lesson of democracy."

The Objectives Resolution was a resolution adopted on 12 March 1949 by the Constituent Assembly of Pakistan. The resolution, proposed by the Prime Minister, Liaquat Ali Khan, proclaimed that the future constitution of Pakistan would not be modeled entirely on a European pattern, but on the ideology and democratic faith of Islam.
Objective Resolution and Liaquat Ali Khan
While introducing the resolution in the constituent Assembly, Liaquat Ali Khan said:
The ideals that promised the demand for Pakistan should form the corner stone of the state. When we use the word “Democracy” in the Islamic sense it pervades all aspects of life. It relates to the system of government and to our society with equal validity because one of the greatest contributions of Islam has been the equality of all men.

Importance of Objective Resolution
This resolution is of fundamental importance in the history of constitutions making in Pakistan because from the first constitution of 1956 till the constitution of 1973 (present constitution) whatever constitution was framed it was based on this objective resolution. At the time it was passed, Mr. Liaquat Ali Khan called it
The most important occasion in the life of this country, next in importance only to be achievement of independence.
It contains those steps and principles which were to be taken for the fulfillment of the basic aim of the freedom struggle that is the establishment of an Islamic Society in Pakistan. Hence, it is a significant document in the constitutional history of Pakistan. When Liaquat Ali Khan visited America in the course of his speech at New Orleans, he said
We believe in God and his Supreme Sovereignity because we believe that civic life must have an ethical content and a higher purpose. But democracy, social justice, equality of opportunity and equality before the law of all citizens inrespective of their race and creed are also aspects of faith with us
Features of Objective Resolution
Importance in the constitutional history of Pakistan

The first principle which comes after the opening Bismillah is the Resolution declared the sovereignty of God as the distinctive political philosophy and the primary feature of the Islamic political system that the God Almighty is the source of authority and power for the whole Universe. This notion that the authority or the sovereignty belongs to Allah is different from the notion that is practiced in the Western Democracy. The Western democracy gives the notion that sovereignty lies in the people but this Resolution is important having the concept of the sovereignty of God. It clarified that people would utilize powers gifted by God so they would have to work within the limits prescribed by Him which is the source of ultimate power and this principle. In fact, this sentence that the sovereignty belongs to Almighty Allah is incorporated in all the constitutions of Pakistan. The exercise of the powers is a sacred trust.
The next line which we have outlined while discussing the principles is an extension of this principle, when you say sovereignty belongs to Almighty Allah authority in this World. The Objective Resolution and later on the all the constitutions of Pakistan recognized, a logical follow up is that the power and the authority that is to be exercised by the state of Pakistan or those who will be exercising power in the name of the state of Pakistan will have to function within the limits prescribed by Allah. They can’t violate His command and principles which have to be followed at all times and this job of exercising authority or power is a sacred trust. Nobody, any leader or institution can claim that his power or authority belongs to him or her. It is a responsibility and an obligation and as an obligation it is a sacred trust because ultimate power belongs to Allah and if you are exercising it then it would be a trust on you, it is your duty not your personal power.
The resolution remained preamble of all constitutions
Due to its importance.The sovereignty belongs to Alimghty Allah is incorporated in all the constitution of pakistan
When Laquat Ali Khan visted America, in the course of his speach at New Orleans,He said,
"We believe in God and his Supreme sovereignty because we believe that civic life must have an ethical content and a higher purpose. But democracy, social justice, equality of opportunity and equality before the law of all citizens irrespective of their race and creed are also aspects of faith with us."

CS304 Assignment # 4 Idea Solution Juns 2012

#include<string.h>
#include<stdlib.h>
#include<iostream>
using namespace std;
//User Class
class User{
// Data members of user class
int Id;
char * name;
//Public interface of user class
public:
//Default Constructor
User(){
Id=-1;
name=NULL;
}
//parametrized constructor
User(int id, char *name){
Id=id;
this->name=new char[strlen(name)+1];
strcpy(this->name,name);
}
//Setter and Getter functions
void setId(int id) {
Id = id;
}
int getID(){
return Id;
}
void setName(char *name) {
this->name=new char[strlen(name)+1];
strcpy(this->name,name);
}
char * getName(){
return name;
}
void playTrack()
{
cout" Start playing the current track";
} };
class Listener :: public User;
{
public: void playTrack()
{
cout" Overloaded Method…";
cout" Start playing the current track";
} };
//Administrator Class class Administrator : public User{ // Data members of user class char * Password; //Public interface of user class
public: void getPassword(char * password)
{
cout" Map password in DB";
cout" Allow access to the system accordingly";
} /* Following code requires existence of Track, Album, Artist, and MusicCategory Classes to be implemented for execution*/ /* //Manipulating interfaces for Track
Track * addTrack()
{
cout"\n***************************************** \n";
cout"\n Adding new Track using add method";
cout"\n***************************************** \n";
Track track = new Track("Track Title"); return track;
}
void deleteTrack(Track * track)
{
cout"\n***************************************** \n";
cout"\n Deleting the Track"/p>

Answer No .1

a) The probability density function of a random variable is given as

F(x) = 2(x-1) 1<x<2

0 Elsewhere

Calculate second moment about origin=?

(As we know the moment about origin)

u_{1 =}E (x) ……… first moment

u_{2 =}E (x) ………. second moment

u_3
= E (x)…………third moment

u_{4 =}E (x)…………fourth moment

As per rave

P (z≥-1.1)

-1.1 se bare

In the second diagram 0.5+0.5=1

Shaded area is raga

In the third diagram

P (z≥ -1.1) =0.5+0.3643

=0.8643 Answer

Second Moment about Origin

Second moment about origin = E (x²)

E (x²) = _-∞ ∫^∞x^2. f(x) dx

E (x²) = ₁∫²x^2.2 (x+1) dx

E (x²) = 2₁∫²x². (x-1) dx

E (x²) = 2₁∫²(x³ – x²) dx

E (x²) = 2 [x⁴/5 – x³/3]²

E (x²) = 2 [(2)⁴/4 – (2)³/3 - ( (1)⁴/4 – (1)³/3 ) ]

E (x²) = 2 (48-32/12) - (3-9/12)

E (x²) = 2 [16/12 + 1/12]

E (x²) = 2 (17/12)

E (x²) = 17/6 Answer

Part b)

F (x,y) = x (1+3y²) / 4

= 0 , elsewhere

0 < x < 2 , 0 < y < 1

Find the marginal probability density function of x =?

g(x) = _-∞ ∫^∞ f (x,y) dy

0 < y < 1

= ₀ ∫¹x (1+ 3y²) /4 .dy

= 1/4 ₀ ∫¹(x + 3xy²) dy

Y=1

= 1/4 [ xy+ 3xy³/3]¹₀

= 1/4 [xy +xy³]¹

=1/4 [x(1) + x(1)³ – (x(0) + x(0)³]

=1/4 [x+x-0]

=1/4 (2x)

G(x) = x/2 for (0 < x < 2)

Answer No.2

a) what is the probability that a poker hand of 5 cards contain exactly 2 Aces ?

n (S) = ⁵²C₅

Let a donate exactly 2 aces

(⁴C₂) (⁴⁸C₃)

P(A) = ______________

(⁵²C₅)

P(A)= 6 (17296)

2598960

103776

P(A)= ______ Answer

2598960

Part b)

A pair of dice is rolled 180 times. By using the normal approximation to binominal distribution , find the probability of a total of 7 occurs at least 25 times ?

Probability of 7 is

(1,6) (2,5) (3,4) (4,3) (5,2) (6,1)

P = 6/36 = 1/36

Now

n=180

p= 1/6

q= 1-p = 1-1/6 = 5/6

µ = n p =180*1/6 =30

♪ = √ n p q

♪ = √ 180*1/6*5/6

♪ = 5

Now

Z = X - µ

♪

Z= X-30

5

At least 25 times

Which means

P (x ≥ 25)

Continuity correction

Working Notes

when we go to continuous form discrete we add or less 0.5

In this case he said at least 25 times which means 25 is include that is why we less 0.5 from 25 for continuity correction.

P ( x ≥ 24.5)

Now

Z = X - µ

♪

Z = X-30

5

Z = 24.5 – 30

5

Z = -1.1

Now

Go to page # 225 of Sta301 handouts and see the value of 1.1 in 0 column.

Because it is 1.10 last pay zero ha agar 1.12 rate ho to 1.1 ki value column 2 me dekhein.

Now 1.1 in column zero = 0.3643

Is ka matlab ha k origin say -1.1 ka fasla 0.3643 ha.

CS302 spring 2012

Assignment No. 4

Due Date:

Your assignment must be uploaded/submitted before or on 25th June, 2012.

Total Marks: 20

Rules for Marking:

It should be clear that your assignment will not get any credit if:

The assignment is submitted after due date.

The submitted assignment file is corrupted.

The assignment is copied.

The assignment material is directly copied from internet.

Objective:

The objective of this assignment is to prepare students to familiar with making next state table for Moore’s machine and designing 4 bit up and down counters using D flip flops.

Q1 Marks 6

State diagram of a Moore machine is given below; draw the next state table of this Moore machine (starting from state 101).

Solution:

Present State			Next State
Q2	Q1	Q0	Q2	Q1	Q0
1	0	1	1	0	0
1	0	0	0	0	1
0	0	1	0	1	0
0	1	0	1	0	1

Q2 Marks 7 + 7 = 14

Give the input tables for both 4 bit up counter and 4 bit down counter consisting of D type flip flops.

Solution:

Present State				Next State				D Flip Flop Input
Q3	Q2	Q1	Q0	Q3	Q2	Q1	Q0	D3	D2	D1	D0
0	0	0	1	0	0	0	0	0	0	0	0
0	0	0	0	0	0	1	1	0	0	1	1
0	0	1	1	0	0	1	0	0	0	1	0
0	0	1	0	0	1	0	1	0	1	0	1
0	1	0	1	0	1	0	0	0	1	0	0
0	1	0	0	0	1	1	1	0	1	1	1
0	1	1	1	0	1	1	0	0	1	1	0
0	1	1	0	1	0	0	1	1	0	0	1
1	0	0	1	1	0	0	0	1	0	0	0
1	0	0	0	1	0	1	1	1	0	1	1
1	0	1	1	1	0	1	0	1	0	1	0
1	0	1	0	1	1	0	1	1	1	0	1
1	1	0	1	1	1	0	0	1	1	0	0
1	1	0	0	1	1	1	1	1	1	1	1
1	1	1	1	1	1	1	0	1	1	1	0
1	1	1	0	0	0	0	1	0	0	0	1

D Flip Flop input table for 4 bit up counter

Present State				Next State				D Flip Flop Input
Q3	Q2	Q1	Q0	Q3	Q2	Q1	Q0	D3	D2	D1	D0
0	0	0	1	1	1	1	0	1	1	1	0
0	0	0	0	0	0	0	1	0	0	0	1
0	0	1	1	0	0	0	0	0	0	0	0
0	0	1	0	0	0	1	1	0	0	0	1
0	1	0	1	0	0	1	0	0	0	1	0
0	1	0	0	0	1	0	1	0	1	0	1
0	1	1	1	0	1	0	0	0	1	0	0
0	1	1	0	0	1	1	1	0	1	1	1
1	0	0	1	0	1	1	0	0	1	1	0
1	0	0	0	1	0	0	1	1	0	0	1
1	0	1	1	1	0	0	0	1	0	0	0
1	0	1	0	1	0	1	1	1	0	1	1
1	1	0	1	1	0	1	0	1	0	1	0
1	1	0	0	1	1	0	1	1	1	0	1
1	1	1	1	1	1	0	0	1	1	0	0
1	1	1	0	1	1	1	1	1	1	1	1

D Flip Flop input table for 4 bit down counter

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