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Posted By: santosh Member Level: Bronze Posted Date: 13 Dec 2007
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2007 Karnataka University BCA Degree Examination (subject is Numerical and Statistical Methods) Question paper
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Define Numerical Integration.
Write the formula for trapezoidal rule.
Given that:
x
y
Find and L!.. atx= 1.6. dx dX
1.4 1.5 1.6
9.451 9.750 10.031
(d) Evaluate . dx 2 by Simpson’s rc1 rule.
0 3
(2+2÷6+6= l6marks)
(Pages :2) 8360—203 (II S BCA (Rev.)) May 2007 SECOND SEMESTER B.C.A. DEGREE EXAMINATION, 2007
NUMERICAL AND STATISTICAL METHODS
Time : Three Hours - Maximum: 80 Marks
Answer any five of the following.
Calculators are allowed.
I. (a) Differentiate Algebraic and Transcendental equations.
(b) Explain Bisection method to the root of an equation f(x) = 0, with example.
(c) Using Newton’s iterative method, find the real root of x log x = 1.2. Carry out four iterations.
(2 + 6+ 8 = 16 marks)
II (a) Define eigenvalue and eigenvector
(b) Using Gauss Jordan method, solve the following system:— 2x+ y+ z=10
3x + 2y + 3z =- 1-8
x. +.4y + 9z = 16.
(c) Explain LU decomposition method to solve the system of imear equations
(2+ 6+ 8= 16 marks)
HI. (a) Define the shift operator E and establish the relation V El—
(b) Derive the Newton’s forward difference interpolation formula.
(c) Given the values:
x : 5 7. 11 13 17
1(x): 150 392 1452 2366 5202
Evaluate f(9), using Lagrange’s formula
(d) Explain curve fitting of a straight line Y = a + bx by least 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? Give an eñmple.
(c) What is regression ? Explain.
(d) Find the coefficient of skewness from the following data
x : 6 12 18 24 30 36 42 y: 4791815105
(3 + 3 + 3 + 7 = 16 marks)
VI (a) Define equally likely events with example
(b) State and prove Baye’s theorem
(c) Two cards are drawn in succession from a pack of 52 cards. Find the chance that the first is a King and the second a queen if the first card is (i) replaced ; (ii) not replaced.
(d) Define sample space. Give example.
(3 +5+5 + 3= 16 marks)
VII. (a) Define Random variable and its mathematical expectation.
(b) A throws a fair die once. If the number obtained is divisible by 3, he gets Es. 9, otherwise, he loses Es 3 Fmd his expectation
(c) State and prove multiplication theorem on expectation.
(d) X is a random variable and a and b are two constants. Then show that
(i) E(aX)=aE(X).
(ii) E(aX+b)=aE(X)+b.
(3 ÷ 3 +6 +4= 16 marks)
VIII (a) Write the probabthty Mass Function for Poisson distribution
(b) In a large consignment of electric lamps, 5 % are defective. A random sample of 8 lamps is thken for inspection. What is the probability that it has one 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)
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