Course Code : MCSE004
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 vivavoce. 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 Simpon‟s 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
NewtonRaphson‟s
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
leastsquares regression line of y on x.
(iii) Find the
leastsquares 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:
10x_{1}
– x_{2} + 2x_{3} = 4
x_{1} + 10x_{2} –x_{3}
= 3
2x_{1}
+ 3x_{2} + 20x_{3} = 7
using the Gauss
elimination method.
(b) Solve the
questions:
10x_{1}
– x_{2} + 2x_{3} = 4
x_{1} + 10x_{2} –x_{3}
= 3
2x_{1}
+ 3x_{2} + 20x_{3} = 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?
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