Karnatak University 2007 BCA (subject is Numerical and Statistical Methods) - Question Paper

describe Numerical Integration.
Write the formula for trapezoidal rule.
provided that:
x
y
obtain and L!.. atx= 1.6. dx dX
1.4 1.5 1.6
9.451 9.750 10.031
(d) Evaluate . dx two by Simpson’s rc1 rule.
0 3
(2+2÷6+6= l6marks)
(Pages :2) 8360—203 (II S BCA (Rev.)) May 2007 2nd SEMESTER B.C.A. DEGREE EXAMINATION, 2007
NUMERICAL AND STATISTICAL METHODS
Time : 3 Hours - Maximum: 80 Marks
ans any 5 of the subsequent.
Calculators are allowed.
I. (a) Differentiate Algebraic and Transcendental equations.
(b) discuss Bisection method to the root of an formula f(x) = 0, with example.
(c) Using Newton’s iterative method, obtain the real root of x log x = 1.2. Carry out 4 iterations.
(2 + 6+ eight = 16 marks)
II (a) describe eigenvalue and eigenvector
(b) Using Gauss Jordan method, solve the subsequent system:— 2x+ y+ z=10
3x + 2y + 3z =- 1-8
x. +.4y + 9z = 16.
(c) discuss LU decomposition method to solve the system of imear equations
(2+ 6+ 8= 16 marks)
HI. (a) describe the shift operator E and establish the relation V El—
(b) Derive the Newton’s forward difference interpolation formula.
(c) provided the values:
x : 5 7. 11 13 17
1(x): 150 392 1452 2366 5202
Evaluate f(9), using Lagrange’s formula
(d) discuss curve fitting of a straight line Y = a + bx by lowest squares procedure..
- (3+4+4+.5=
IV. (a)
(b)
(c)
1.0 1.1 1.2 1.3
7.989 8.403 8.781 9.129
Tu over2 8360—203 (II S BCA (Rev.)) May 2007
V. (a) What do you mean by “Central tendency” and “Measure of central tendency”?
(b) What is correlation? provide an eñmple.
(c) What is regression ? discuss.
(d) obtain the coefficient of skewness from the subsequent data
x : six 12 18 24 30 36 42 y: 4791815105
(3 + three + three + seven = 16 marks)
VI (a) describe equally likely events with example
(b) State and prove Baye’s theorem
(c) 2 cards are drawn in succession from a pack of 52 cards. obtain the chance that the 1st is a King and the 2nd a queen if the 1st card is (i) changed ; (ii) not changed.
(d) describe sample space. provide example.
(3 +5+5 + 3= 16 marks)
VII. (a) describe Random variable and its mathematical expectation.
(b) A throws a fair die once. If the number found is divisible by 3, he gets Es. 9, otherwise, he loses Es three Fmd his expectation
(c) State and prove multiplication theorem on expectation.
(d) X is a random variable and a and b are 2 constants. Then show that
(i) E(aX)=aE(X).
(ii) E(aX+b)=aE(X)+b.
(3 ÷ three +6 +4= 16 marks)
VIII (a) Write the probabthty Mass Function for Poisson distribution
(b) In a large consignment of electric lamps, five % are defective. A random sample of eight lamps is thken for inspection. What is the probability that it has 1 or more defectives?
(c) Write the properties of Normal distribution.
(d) What do you mean by IFR and DFR.
(2 + 3+8+3= 16 marks)

Earning:   Approval pending.