Test Papers / Previous Question Papers of IGNOU CS08 Numerical and Statistical Computing December 2005

ADCA / MCA (II Yr)
Term-End Examination

December, 2005

CS08 : Numerical and Statistical Computing

Time: 3 hours
Maximum Marks: 75

1. (a) (a) Explain why the following are wrong :
(i) 6.0 E - 30 (a const.)
(ii) 2ABC (a variable name)
(iii) A * B = A + B (assignment statement)

(b) Write down the FORTRAN equivalent for the following mathematical expressions : (3)
(i) p - 3^q-1+log_e4
(ii) l p³+√3 l
(iii) e^-x2/2/√2π

(c) Indicate the error in the following : (3)
(i) IF (A = B) THEN
(ii) x= SIN(45º)
(iii) Y = ALOG (2/3)

(d) Let P, Q, R and W be logical variables and P = .TRUE., Q = .FALSE., R =.TRUE. Find the value of W in the following : (3)
(i) W = P .AND. R .OR. .NOT. Q
(ii) W = .NOT. P .AND. .NOT. Q .OR. .NOT. R
(iii) W = P .AND. .NOT. Q .AND. .NOT. R

(e) Read an integer array of N(≤ 100) numbers Write a program segment to compute the average in whole number (no fraction) and print the average value as AVERAGE = < value >.
You can assume N is already stored in the computer memory. (3)

(f) Write a program segment to multiply two matrices A (l x m) and B (m x n) and form a new matrix C. You can assume that A, B and C are already declared in the Program. (3)

(g) A card is drawn from a pack of cards. What is the probability that it is either red or a king ? (3)

(h) Find the s.d. of a series X for which ΣX_r = 50, ΣX_r² = 1000 and r = 1(1)5. (3)

(i) Find the mean values of the variables X and Y from the following regression equations :
4X - 5Y = 33
20X - 9Y = 107

(j) Fit a straight line y = a + bx by the method of least squares on the points (2, 10), (4, 20), (6, 25). (3)

2. (a) We want to classify the people in three groups according to their ages in the following manner : (7)
group1 = age ≤ 30; group2 = 30 < age ≤ 60 group3 = 60 < age .
Write a program which reads the ages of 1000 people, one by one, and puts it in the appropriate group. Print the number of people in each group. Use ELSEIF.

(b) Wriie a program for Computing n_Ck = n!/k!(n-k)!. Print its value. Read N and K. (8)

3. (a) Write a program segment to read N (≤ 1000) and N values in an array and find the maximum value. Print the value and its location in the array. (7)

(b) Compute the regression coefficients b_yx and b_xy, and the coefficient of correlation for the following data : (8)

Also write down the regression equation of Y on X.

4. (a) Read 100 pairs of values (X_i, F_i), i = 1, 2, ... 100 as two arrays where X_i denotes the value of the variate X and F_i its frequency. Write a program to compute Arithmetic Mean (AM) and Standard Deviation (SD). Print AM and SD. (8)

(b) Calculate the median and mode for the following data : (7)

5. (a) Box1 contains 3 white and 7 black balls and Box2 contains one white and 9 black balls. A box is selected at random and a ball is drawn. (7)
(i) What is the probability that the ball drawn is white ?
(ii) If the ball drawn is white, what is the Probability that it was drawn from Box1 ?

(b) Let p_0j be the price of quantity q_0j of commodity j in the base year. Let the corresponding figures for the current year be p_1j and q_1j, respectively. Write down the four formulae for calculating the Price Index Number P₀₁. (8)
The following data is colllected for the years 2001 and 2002 for family expenditure :

Calculate the Cost of Living Index Number in 2002 as compared to 2001.