Q.
1. How do you use differential equations in economics? What type of situations can be helpfully depicted using differential equations? Discuss the role of initial condition in solving a differential equation. If your objective is to examine the stability of equilibrium, with the help of an example, show how a second-order differential equation helps in addressing your concern.
2. Give examples of problems where you can make use of Poisson distribution. Does it have a probability density function? Why or why not? Discuss your answer in the context of the rnean and variance of Poisson distribution.
Section B
3. Explain the relevant considerations of making a choice between one-tailed and two-tailed tests. How would you determine the level of significance in the above tests?
4. A linear programming problem is given as
Min z = 30 x1+ 50x2
Subject to
Find its optimal solution.
5. How would you determine linear dependence of a matrix? Define the rank of a matrix in terms of its linear independence.
6. The correlation coefficient between nasal length and stature for a group of 20 Indian adult males was found to be 0.203. Test whether there is any correlation between the characteristics in the population.
7. Write short notes on the following:
a) Eigen-vectors and Eigen-values
b) Taylor’s expansion
c) Mixed strategy
d) Kuhn-Tucker condition
