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Mth202 Assignment No. 4 Solution

Tuesday, January 11, 2011 Posted In Edit This


Assignment 4 Of MTH202 (Fall 2010)




Maximum Marks: 15                                                                                       

                                                                                             
Due Date: January 11, 2011

Q-1:

How many bit strings of length 10 have
a)      Exactly three 0’s?
b)      The same number of 0’s as 1’s?

Q:2

Prove by mathematical induction that for all positive integral values of n, x2n-1 is divisible by x +1 ;( x¹1)

Q:3

Use the Euclidean algorithm to find gcd (1331, 1001)



Question#2 solution

using mathematical induction

step 1: first we will prove that for n =1 it is true

thus x^2n-1 = x^2-1 = (x-1)*(x+1) 

clearly since it has factor of x+1 we can say that x^2n-1 is divisible by x-1

step 2: let assume that for n = k it is true thus

x^2k-1 is divisible by x+1

thus we can write as x^2k-1 = P (x+1) P is quotient

now we have to prove that it is true for n=k+1

step 3: now let n = k+1 thus

x^2(k+1) - 1 = x^(2k+2) - 1 = x^2k*x^2 -1 = (x^2k-1+1)x^2 - 1

(x^2k-1)*x^2 + (x^2-1)

for step 2 we can write above equation as

P (x+1)*x^2 + (x+1)*(x-1) = (x+1)* (Px^2+x-1)

which contain factor of x+1 thus divisible by x+1

thus even it is proved for n=k+1

according to mathematical induction given is true for all integral values of n


Question 3; Marks: 03
Use the Euclidean algorithm to find gcd (1331, 1001)
Solution 
gcd(1331, 1001) = gcd(1001, 330)
= gcd(330, 11)
= gcd(11, 0)
= 11


How many bit strings of length 10 have

a) Exactly three 0’s?

is ka answer hai 10C3 =120

b) The same number of 0’s as 1’s?
is ka answer hai 10 C 5 = 152

Mth302 Assignment No. 2 Announced

Tuesday, January 11, 2011 Posted In Edit This
Assignment # 2

MTH302 (Fall 2010)
Total marks: 10
Lecture # 22 to 33 
Due date: January 17, 2011 
 
DON’T MISS THESE Important instructions:
• Upload assignments properly through LMS, (No Assignment will be accepted through email).
• All students are directed to use the font and style of text as is used in this document.
• This is an individual assignment, not ***** assignment, so keep in mind that you are supposed to submit your own, self made & different assignment even if you discuss the questions with your class fellows. All similar assignments (even with some meaningless modifications) will be awarded zero marks and no excuse will be accepted. This is your responsibility to keep your assignment safe from others. Many solution files sent by students in assignment 1 are found to be copied and so awarded zero. You are therefore reminding here again.

• There are 5 questions in the assignment but only one question will be graded. 


Question 1: (Non-graded)

Find a linear regression line y = ax + b (where a is the slope and b is the y-intercept) 
for values of x and y given below. 


y x

7 3
10 5
11 7
15 9

Question 2: (Non-graded)

Find Quartile Deviation of the following data.

1,2,8,7,10,11,15,20,18,25

Question 3: (Graded) Marks 10

The table below shows the demand for a particular item in a shop for the last nine months.

Month Demand

1 10
2 12
3 13
4 17
5 15
6 19
7 20
8 21
9 20

Calculate a three month moving average. What would be your forecast for the demand in month ten?

Question 4: (Non-graded) 

Calculate the coefficient of variation for data given below.
10, 12, 14, 16, 18, 20

Question 5: (Non-graded)
Calculate the mean, median, mode and range of the data given below.
0, 1, 2, 5, 9, 8, 3, 2, 6

STA301 Assignment No. 3 Solution

Tuesday, January 11, 2011 Posted In Edit This

 Assignment No.3 (Course STA301)

Fall 2010 (Total Marks 30)

for solution CLICK HERE
Thanks to Armaan Makhani, who share this solution with us.

Deadline

Your Assignment must be uploaded/ submitted before or on

23:59, 13th Jan, 2010  

(STUDENTS ARE STRICTLY DIRECTED TO SUBMIT THEIR ASSIGNMENT BEFORE OR BY DUE DATE. NO ASSIGNMNENT AFTER DUE DATE WILL BE ACCEPTED VIA E.MAIL).

Rules for Marking

It should be clear that your Assignment will not get any credit IF:
  • The Assignment submitted, via email, after due date.
  • The submitted Assignment is not found as MS Word document file.
  • There will be unnecessary, extra or irrelevant material.
  • The Statistical notations/symbols are not well-written i.e., without using MathType software.
  • The Assignment will be copied from handouts, internet or from any other student’s file. Copied material (from handouts, any book or by any website) will be awarded ZERO MARKS. It is PLAGIARISM and an Academic Crime.
  • The medium of the course is English. Assignment in Urdu or Roman languages will not be accepted.
  • Assignment means Comprehensive yet precise accurate details about the given topic quoting different sources (books/articles/websites etc.). Do not rely only on handouts. You can take data/information from different authentic sources (like books, magazines, website etc) BUT express/organize all the collected material in YOUR OWN WORDS. Only then you will get good marks.

 

Objective(s) of this Assignment:


  • The assignment is being uploaded to strengthen the students’ basic concepts about probability distributions.

  • The assignment is uploaded to depict the use of discrete and continuous probability functions/distributions.




Assignment No. 3
Question 1                                                                                                2+2+6=10Marks

a)      Define Bernoulli trail and Binomial Experiment.      
b)      In which condition, Poisson distribution is used to approximate hypergeometric       distribution?
c)      Find the probability that (i) No defective bolt (ii) at most 5 defective bolts will be found in a box of 200 bolts if it is known that 2 percent of such bolts are expected to be defective.
     
Question 2                                                                                              3+5+2=10Marks
a) If its rain, an umbrella salesman can earn $ 30 per day. If it is fair, he can lose $ 6 per day. What is his expectation if the probability of rain is 0.3?

b)               Show that the following is a density function.

              f(x)                =                0 < x < 2
                                    = 0                  elsewhere
c)
            






Question 3                                                                                                2+2+6=10Marks
a)      From the following table find P(X + Y < 1);











b)  Write this expression h (3; 70, 20, 5) in probability notations/function.

c) An electrical firm manufactures light bulbs that have a length of life that is normally distributed with mean equal to 800 hours and a standard deviation of 40 hours. Find the probability that
(i) A bulb will burn between 778 and 834 hours.
(ii) A bulb will burn in less than 778 hours.

Mgt601 GDB Solution

Tuesday, January 11, 2011 Posted In Edit This

Schedule

Opening Date and Time: January 11, 2011 At 12:01 A.M. (Mid-Night)
Closing Date and Time: January 12, 2011 At 11:59 P.M. (Mid-Night)

Note: No extra or bonus/grace period is available for attempting GBD.

Discussion Question

"Ali the owner of a small business is thinking to train his employees in soft skills but he is reluctant as he is not clear about the resultant benefits of such training. You need to convince him to train his employees in soft skills by realizing him the resultant benefits his business will get after such training

Solution:

Following are the points that have to take by Ali to train his employees.

1 the major benefit to train his employees is divide the work of the owner (Ali) and Ali can pay attention on the other important task.

2 things to get the benefit from the training employees are that they have good convincing power so that the customers will be regular.

3 from by the train employees Ali can regular check his account of business and by this regularity his business earn more and more.

4 in the absence of the owner the train employees can take care of the owner work.

Mgt402 Assignment No. 2 solution

Tuesday, January 11, 2011 Posted In Edit This
“ Cost & Management Accounting (MGT402) ”
Assignment No. 02 Marks: 20

PROBLEM:
Mirza & Co manufactures and sells 3,500 units of product “A” at a selling price of Rs. 30 per unit. Fixed Cost Rs. 45,000 and variable cost Rs 10 per unit incurred to manufacture the product A.

Management of Mirza & Co. is anxious to improve the company’s profit performance and has asked for analysis of a number of items.

Required:
�� Scenario 1: Calculate contribution margin and net profit with the help of given data.

�� Scenario 2: Refer to original data;the management feels that due to increase of advertising budget by Rs. 30,000 (this cost is considered as fixed cost) would increase sales volume of product “A” by 20%. Should the advertisement budget be increased and show complete calculation of contribution margin and net profit with these changes?

Also compare the findings of scenario 2 with scenario 1and suggest which scenario is more profitable.

�� Scenario 3: Refer to original data the management decided to improve the quality of its product “A” by increasing the variable cost by 40%. Due to improvement in quality of product the sales volume also increased by 20%. What effects should be seen on its Contribution margin and net profit with new these changes.

Also compare the findings of scenario 3 with scenario 1 and suggest which scenario will more profitable.

�� Scenario 4: Refer to original data; management has a plan to increase the sale price of the product “A” by 25%. Due to this, they expect that their sales volume decreased by 30%. Analyze the all changes by preparing income statement.

Also compare the findings of scenario 4 with scenario 1 and suggest which scenario is more profitable.

Schedule
Opening Date and Time: January 10, 2011 At 12:00 A.M. (Mid-Night)
Due Date and Time: January 13, 2011 At 11:59 P.M. (Mid-Night)
...................
solution:
if this solution is not visible correctly, you may click here to DOWNLOAD the file


Assignment no.2 Mgt-402
Cost and management

PROBLEM:
Mirza & Co manufactures and sells 3,500 units of product “A” at a selling price of Rs.
30 per unit. Fixed Cost Rs. 45,000 and variable cost Rs 10 per unit incurred to
manufacture the product A.
Management of Mirza & Co. is anxious to improve the company’s profit performance
and has asked for analysis of a number of items.
Required:
v Scenario 1: Calculate contribution margin and net profit with the help of given data

Solution.


Sales                            (3500*30)                    RS.105, 000

Less. Variable cost      (3500*10)                    RS.35000

Contribution margin                                     70,000

Less. Fixed cost                                              45,000

Profit                                                              25,000



Scenario 2:
 Refer to original data; the management feels that due to increase of
advertising budget by Rs. 30,000 (this cost is considered as fixed cost) would increase
sales volume of product “A” by 20%. Should the advertisement budget be increased and  show complete calculation of contribution margin and net profit with these changes?
Also compare the findings of scenario 2 with scenario 1 and suggest which scenario is more profitable.

Increasae in advertising budget by 30,000
Fixed cost will increase from 45000 to 45000+30,000=75,000 RS.
Sales volume increased by 20%=3500+3500*20%=4200 units
                                    Scenario 1                  scenario 2.
Sales                            3500*30=105,000       4200*30=126,000
Veriable cost               3500*10=35000          4200*10=42000
Contribution margin             70,000                         84000
Fixed cost                               45000                          75000
Profit                                      25000                          9,000

Analysis.
According to this analysis, the changes should not be made because net profit is low, so scenario 1 is more profitable.


v Scenario 3:
Refer to original data the management decided to improve the quality of its  product “A” by increasing the variable cost by 40%. Due to improvement in quality of product the sales volume also increased by 20%. What effects should be seen on its Contribution margin and net profit with new these changes.
Also compare the findings of scenario 3 with scenario 1 and suggest which scenario
will more profitable.

In this scenario variable cost will increase by 40%
So variable cost will be =10+10*40%=14 RS.
Sales volume increased by 20%=3500+3500*20%=4200 units

                        Scenario 1                  scenario 3.
Sales                3500*30=105,000       4200*30=126,000
Veriable cost   3500*10=35000          4200*14=58,800
Contribution
margin                        70,000                         67200
Fixed cost                   45000                          45000
Profit                          25000                          22,200

Analysis.
According to this analysis, the changes should not be made because net profit is low, so scenario 1 is more profitable

v Scenario 4:
Refer to original data; management has a plan to increase the sale price of the product “A” by 25%. Due to this, they expect that their sales volume decreased by 30%. Analyze the all changes by preparing income statement.
Also compare the findings of scenario 4 with scenario 1 and suggest which scenario is more profitable.

Increase in sale price by 25% then sale price will be=30+30*25%=38RS
Sales volume decrease by 30% then sales will be=3500-3500*30%=2450


                                    Scenario 1                  scenario 4.
Sales                            3500*30=105,000       2450*38=93100
Veriable cost               3500*10=35000          2450*10=24500
Contrbtion margin                70,000                         68600
Fixed cost                               45000                          45000
Profit                                      25000                          23600

Analysis.
According to this analysis, the changes should not be made because net profit is low, so scenario 1 is more profitable



Analyze the all changes by preparing income statement


                                    Scenario 1       scenario 2       scenario 3       scenario.4
Sales                            105,000           126000            126000            93100
Veriable cost               35000              42000              58800              24500
Contribution margin 70,000             84000              67200              68600
Fixed cost                   45000              75000              45000              45000
Profit                          25000              9000                22200              23600

..............
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