Netaji Subhas Open University (NSOU) 2009 M.C.A Statistics & Numerical Techniques - Question Paper
MCA 2.3
MCA (2nd Semester)
Term End exam – December, 2009
Statistics & Numerical Techniques
Paper – 2.3
Time : two Hours Full Marks : 50
Brief Summary of the ques. paper : It consists of total eight ques. of which ques. no. 5(a)
contains a few graphical symbols.
Paper 2.3
Answer any five questions :
1. a) Prove that the relative error of a product of three non-zero numbers does not exceed the sum of the relative errors of the given numbers. [Marks 5]
b) Explain the different types of Errors. [Marks 5]
2. a) Explain the Newton-Raphson algorithm for finding the roots of equations. [Marks 6]
b) Use Newton-Raphson method to find a root of the equation x3 2x 5 = 0 [Marks 4]
3. a) Solve using Gauss elimination method : [Marks 8]
5x - 2y + z = 4
7x + y 3z = 8
3x + 7y + 4z = 10
b) What are Linear and Polynomial interpolations ? [Marks 2]
4. a) Calculate f (0.4) using the table : [Marks 5]
|
X
f(X) |
0.3
0.61 |
0.5
0.69 |
0.6
0.72 |
b) Given the following table of values of y = f(x)
|
X |
0 |
5 |
10 |
15 |
20 |
|
f(X) |
1.0 |
1.6 |
3.8 |
8.2 |
15.4 |
Construct the difference table and compute f(21) by Newton's Backward difference
interpolation formula. [Marks 5]
5. a) Evaluate 1 X2 dx , by both Trapezodial and Simpson's rule with h = 0.25 [Marks 8]
b) What is Numerical Differentiation and Integration ? [Marks 2]
6. a) Define discrete random variable with an example. [Marks 4]
b) A random variable X assumes the values -1, 0, 1 with probability 1/3, 1/2, 1/6
respectively. Determine the distribution of X. [Marks 4]
c) Define correlation coefficient. [Marks 2]
7. a) Explain Poisson Distribution with an example [Marks 7]
b) Explain Positive Correlation, Negative Correlation and Zero Correlation. [Marks 3]
8. a) Fit the exponential curve y = aebx to the following data (e = 2.71828) [Marks 6]
|
X |
0 |
2 |
4 |
|
Y |
5.012 |
10 |
31.62 |
b) From the Taylor series for y(x), find y(0.1) correct to four decimal places if y(x) satisfies
y' = x y2 and y (0) = 1. [Marks 4]
| Earning: Approval pending. |
