

CS  08 Numerical & Statistical Computing

Item 
Amount in (Rs.) 

Food 
2000 
Room Rent 
1000 
Transport 
500 
Books/Stationery 
500 
Maintenance 
1000 
(g) Explain the concepts of 'skewness' and 'kurtosis' along with
their significance in the study of distribution of mass of data. (4)
(h) A computer while calculating the correlation coefficient between
20 pairs of two variables x and y obtain the following results: (5)
n = 20, å x = 100, å
y = 80, å x^{2 }= 520, å
y^{2 } = 360, å xy = 420
It was later discovered at the time of checking that he had copied down two pairs as:
x 
y 
While the correct values were: 
x 
y 

6 
4 
8 
12 

8 
6 
6 
8 
Obtain the correct value of correlation coefficient.
(i) Two dice are thrown. Find the probability that sum of the numbers on two dice is 9, given that first dice shows 6. (3)
2. (a) Write a FORTRAN 90 program that reads an ndigit number (for a positive integer n) and reverses the digits of the number to obtain a new number (e.g., if number 24379 is read then the new number obtained by reversing the digits is 97342). The program then prints the result with a suitable message. (8)
(b) Write a FORTRAN program that goes on reading values for an integer variable N until the value read is zero or negative. For each positive value of N read, the program tests whether N is a prime number or not. Also it should print appropriate messages. (7)
3. (a) Write a FORTRAN program that goes on reading sets of three real values until at least one of the values in any set of three values is zero or negative. The three values in a set denote lengths of the sides of a triangle. The program tests whether the triangle represented by the values is an equilateral triangle. If the triangle is equilateral then it computes the area of the triangle. If the triangle represented is not equilateral then it finds the perimeter of the triangle. Program prints suitable messages also. (7)
(b) Calculate the variance for the classfrequency distribution given below: (4)
Marks obtained 
Number of students 

010 
15 
1020 
20 
2030 
25 
3040 
17 
4050 
12 
(c) The income of 80 families are given below: (4)
Income 
No. of families 

4000  6000 
8 
6000  8000 
24 
8000  10000 
32 
10000  12000 
16 
4. (a) A fivefigure number is obtained by the digits 0, 1, 2, 3,
4 (without repetition). Find the probability that the number formed is
divisible by 4. (6)
(b) The average number of radioactive particles through a counter during 1 milli second in a laboratory experiment is 3. What is the probability that five particles enter the counter in a given millisecond? (4)
(c) The probability of a college student being male is 1/3 and that of being female is 2/3. The probability that a male student completes the course is 3/4 and that a female student does it is 1/2. A student is selected at random and is found to have completed the course. What is the probability that the student is a male? (5)
5. (a) Fit a straight line trend by the method of least squares to the following data: (7)
Year : 
1951 
52 
53 
54 
55 
56 
Price Index : 
107 
110 
114 
112 
115 
113 
(b) The following table gives the average wholesale prices of the four grains for the years 1998 to 2001. Compute chain base index number. (8)
Grain 
1998 
1999 
2000 
2001 

Rice 
12 
18 
24 
12 
Wheat 
18 
36 
54 
24 
Gram 
12 
36 
60 
24 
Barley 
15 
21 
54 
33 
6. (a) Compute the approximate value of the integral
I =(1
+ x + x^{2}) dx
using Simpson's rule by taking interval size h as 1. (7)
(b) Find the value of cosh = d/dx (sinh x) at x = 1.52 from the following table: (8)
x 
sinh x 

1.5 
2.129279 
1.6 
2.375568 
1.7 
2.645632 
1.8 
2.942174 
1.9 
3.268163 
2.0 
3.626860 




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