Numerical and Statistical Computing.pdf - Google Drive
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Numerical and Statistical Computing.pdf - Google Drive
Page 1 of 4. I MCSE-004 I. MCA (Revised). Term-End Examination. December, 2009. MCSE-004 : NUMERICAL AND STATISTICAL. CO
I MCSE-004 I
MCA (Revised) Term-End Examination December, 2009 MCSE-004 : NUMERICAL AND STATISTICAL COMPUTING Maximum Marks : 100
Time : 3 hours
Note : Question number 1 is compulsory. Attempt any three from the rest. Use of calculator is allowed.
1.
(a) Explain truncation error. Show that 2+6 a(b—c) ab— ac, where : a = .05555 El b =.4545 El c = .4535 El Use bisection Method to find a root of the equation x3 — 4x — 9 =0
8
Go upto 5 - iteration only.
Use Gauss - Elimination method to solve the following system of equations :
8
x1 + x2 + x3 =3 4X 1 + 3X 2 + 4X3 = 8
9x1 + 3x2 + 4x3 = 7 MCSE-004
1
P.T.O.
Evaluate f(15), Given the following table of values : x
-
f(x) -
8
10 20 30 40 50 46 66 81 93 101
Calculate the value of the integral,
8
5.2
f log x 4
dx
by.
Trapezoidal rule. Waddles' rule. *(Take h =0.2).
2.
(a) Find a root (correct to three decimal place) of x3 — 5x +3 =0 by Newton-Raphson method. Use Jacobi's method to solve the equation :
8
8
20x+y-2z=17 3x +20y — z = —18 2x —3y +20z =25 Explain the bisection method. MCSE-004
2
4
3.
(a) Given :
5+3
(x)=sin(x) f
(0.1) = 0.09983, f (0.2) = 0.19867
Use method of Lagrange's interpolation to find f(0.16). Find error in f(0.16). Evaluate . dx Use Gauss-Legendre three 1+x 0 point formula. Explain initial value problem with an example.
8
4
6 4.
(a) Evaluate 5[ 2 + sin (2 .J) ]
dx
using
10
simpsons' rule with 11 points. (b) Solve the initial value problem
10
u1 = — 2tu2 with u(0) =1 and h= 0.2 on the interval [0,1]. Use Fourth order classical Runge Kutta method. 5.
(a) A farmer buys a quantity of cabbage seeds from a company that claims that approximately 90% of the seeds will germinate if planted properly. If four seeds are planted, what is the probability that exactly two will germinate ?
MCSE-004
3
8
P.T.O.
(b) In a partially destroyed laboratory record of an analysis of correlation data, the following results only are legible.
8
Variance of x = 9 Regression equation : 8x —10y + 66 = 0 40x — 18y — 214 = 0 What are Mean value of x and y. Correlation coefficient between x and y. (iii) Standard deviation of y. (c) Suppose that the amount of time one spends in a bank to withdraw cash from an evening counter is exponentially distributed with mean ten minutes, that is X = 110. What is the probability that the customer will spend more than 15 minutes in the counter ? -o0o-
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