August 2012

Master of Computer Application (MCA) – Semester 3

MC0074 –Statistical and Numerical methods using C++– 4 Credits

(Book ID: B0812)

Assignment Set – 1 (60 Marks)

Answer all Questions Each Question Carries 10 Marks 1. An experiment succeeds twice as often as it fails . Find the chance that in the next six trials there will be atleast four successes.

2. Find E(x), E(X2) and 2 for the probability function P(x) defined by the following table. (k is

constant)

xi 1 2 3 ……….. N

P(xi) k 2k 3k …………… Nk

3. An insurance company has discovered that only about 0.1% of the population is involved in

a certain type of accident each year. If its 10000 policy holders were randomly selected from

the population, what is the probability that not more than 5 of its clients are involved in such an

accident next year?

4. Find the moment generating function of random variable which is uniformly distributed over

(–a, a). Evaluate E(X2n).

5. By the method of least squares, fit a straight line for the following data:

x 1 2 3 4 5

y 14 13 9 5 2

6. Briefly explain Markov chains.

August 2012

Master of Computer Application (MCA) – Semester 3

MC0074 –Statistical and Numerical methods using C++– 4 Credits

(Book ID: B0812)

Assignment Set – 2 (60 Marks)

Answer all Questions Each Question Carries 10 Marks 1. A civil engineer has measured the height of a 10 floor building as 2950 cms and the working height of each beam as 35 cms while the true values are 2945cms and 30cms respectively. Compare their absolute and relative errors.

2. Compute the adjoint of A and hence find the inverse of A, where

341

431

321

A .

3. Find a real root of the transcendental equation cosx – 3x + 1 = 0 correct to four decimal

places using iteration method.

4. Using Newton’s forward difference formula, find a cubic polynomial which takes the

following values y(0) = 1, y(1) = 0, y(2) = 1 and y(3) = 10. Hence or otherwise, obtain y(0.5).

5. Find dx

dy and

2

2

dx

yd at x = 1 and x = 0 from the following data:

6. Evaluate

1

0

21 x

dx using Trapezoidal rule with h = 0.2. Hence determine the value of .

x 0 2 4 6 8

y 7 13 43 145 367