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Course Code :                                                                MCSE-004
Course Title :                                                                 Numerical and Statistical Computing
Assignment Number :                                                    MCA(5)/E004/Assign/2012
Maximum Marks : 100                                                  Weightage : 25%
Last Dates for Submission :                                          31st October, 2012 (For July 2012 Session
                                                                                       30th April, 2013 (For January 2013 Session)

This assignment has five questions in all and carries 80 marks. The rest of the 20
marks are for viva-voce. Answer all the questions. You may use illustrations and
diagrams to enhance the explanations. Please go through the guidelines regarding
assignments given in the Programme Guide for the format of presentation.

Question 1:
(a) A can solve 90% of the problems given in a book and B can solve 70%.
What is the probability that at least one of them will solve a problem
selected at random?


(b) When a computer uses a number base 2, how many significant decimal
digits are contained in the mantissa of floating numbers?
  
 (c) Evaluate the integral

using (i) composite trapezoidal rule, (ii) composite Simpons rule,
with 2, 4 and 8 equal subintervals.


Question 2: Write the following programme in C language:
(a) Write a programme in C to find a root using bisection method.
Perform the five iterations of the bisection method to obtain the
smallest positive root of the equation f(x) = x3 – 5x +1 = 0,
verify your answer with the programme written by you.

(b) Write a programme in C to find a root using Newton Raphson
Method. Apply Newton-Raphsons method to determine a root of
the equation f (x) = cos x – xex= 0, if exists verify your answer
with the programme written by you.


Question 3:

(a) Find the probability of getting between 6 and 9 tails inclusive in
20 tosses of a fair coin by using (i) the binomial distribution,
(ii) the normal approximation to the binomial distribution.
  



(b) Table 2 below shows the respective heights x and y of a sample of
12 fathers and their oldest sons.
(i) Construct a scatter diagram.
(ii) Find the least-squares regression line of y on x.
(iii) Find the least-squares regression line of x and y.
Table 2
Height x of Father (centimetres)
165
160
170
163
173
158
178
168
173
170
175
180
Height y of Son (centimetres)
173
168
173
165
175
168
173
165
180
170
173
178



(c) Find the area under the standard normal curve (a) between z = 0 and z = 1.2, (b) between z = – 0.68 and z = 0, (c) between z = – 0.46 and z = 2.21, (d) between
z = 0.81and z = 1.94. 

 
Question 4: Solve the following equation (if a solution exists) using given method:
(a) Solve the equation:
10x1x2 + 2x3 = 4
x1 + 10x2x3 = 3
2x1 + 3x2 + 20x3 = 7
using the Gauss elimination method.

(b) Solve the questions:
10x1x2 + 2x3 = 4
x1 + 10x2x3 = 3
2x1 + 3x2 + 20x3 = 7
using the LU decomposition method.

Question 5: Out of the three method i.e. Secant method, Regula Falsi
method and the Newton Raphson method which method is more
efficient and why? Determine the efficiency or the order of these
three methods?


For Solution Click on below Link:
 

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