Assignment 3 (Due: 3 November 2010)

The table at the bottom of the webpage gives the students' roll numbers and the problems assigned to them. The problem numbers are as in the following list.

STATISTICS


1. Find the p-order moments for a given list of numbers. The cases for p = 0, 1, 2, 3, 4 must be implemented.
2. Find the minimum, median and maximum from a given list of numbers.
3. Given two lists of numbers of the same size, compute their statistical and rank correlations
4. Given a set of 2D coordinates (x,y), fit a line y = mx + c using linear regression.
5. Given a set of 2D coordinates (x,y) fit a line y = mx + c using RANSAC (RANdom SAmpling and Consensus) approach.
6. Given a value x, and the mean mu and standard deviation sigma of a Normal Distribution, compute the probability of occurrence of x, the cumulative probability of occurrence of a value v < x, and the cumulative probability of occurrence of a value v > x.
7. Given the probability of success p and the number of trials N, write a function to compute the probability of succeeding k times out of N using the Binomial Distribution. Also, give an option to find the probability of succeeding at least k times.
8. Given a list of numbers read from a file or given on standard input, compute their histogram, cumulative and pareto histograms.


MATRICES AND NUMERICAL METHODS


9. Given two matrices, write functions to add, subtract and multiply them
10. Given a matrix, write a function to compute its eigenvalues and eigenvectors.
11. Given a linear system of equations, find a function to solve them using Gauss-Jordan method.
12. Given a matrix, find its LU-decomposition
13. Write a function to find the roots of an equation using the bisection method
14. Write a function to find the roots of an equation using Ridders method
15. Write a function to find the roots of an equation using Newton-Raphson method
16. Write a function to compute integrals using Simpson's Rule and any one other classical method
17. Write a function to compute integrals using Gaussian Quadrature method.
18. Write a program to compute the Gamma Function
19. Write a program to compute the Beta Function


MULTIPLE PRECISION ARITHMETIC

All the students working on the problems assigned in this section should see me before they start their work.
20. Write functions to add, subtract and multiply long integers
21. Write a function to multiply two long integers. See if you can find an efficient algorithm.
22. Write a function to compute a mod b where a and b are both long integers. Use it to compute inverse of a long integer.
23. Write a function to compute a^b
24. Write a function to compute discrete logarithms, i.e., x when a^x mod b is given along with a and b.
25. Implement two methods to determine if a given long integer is a prime number


TEXT AND DOCUMENT PROCESSING


26. Given a page of text, identify paragraphs, sentences and also their counts (i.e., how many)
27. Given a page of text, identify words and count their frequency. See if you can handle upper and lower cases. Your output should include data of word_length vs. frequency.
28. Write functions to do character level analysis for counting the number of upper, lower-case letters, vowels, consonants, punctuation and any other.
29. Write a function to retrieve a sentence containing a given word or a phrase


MISCELLANEOUS PROBLEMS


30. Given acceleration due to gravity g and the length of a simple pendulum, write a function to compute the time period of oscillation
31. Given a set of (x,y) coordinates, find the area enclosed by them
32. Find the value of sin(x), cos(x) and log(x) given x using any of their series approximations.
33. Given two sets of points, find the distance between the two sets using Hausdorff distance
34. Given a string of text, write a function to compute a CRC (Cyclic Redundancy Check) sum.

Problem Assignment