1. Consider a firm with a production function given as
y 80x1 40x2 2x1^2 3x1x2 2x2^2.

It has a total cost of 96 due to input prices W1 6 and w2 3. Find the maximum output the firm can produce given the cost.

2.(a) What is the difference between a differential equation and a difference equation? Find the solution to the following equation and determine whether the time path followed by it is oscillatory or convergent:

yt 1 1/3 yt (yo

3.(a) State the central limit theorem and explain its practical importance.

(b) Assume that weights of male population follow normal distribution. The mean and standard deviation are 70 kg and 15 kg respectively. If you consider the weight of 50 males, what would be the mean and standard deviation of your sample?

4.(a) State and explain Bayes theorem. For which calculation is the formula important? Calculate P if P 0.25, P 0·4 and P 0·5 using Bayes' theorem.

5. Find the particular solution of dy/dx 2.

6. Show that E E 2b E b^2 if b is a constant. What is the value of b that gives the minimum value of E

7. Show that in Poisson distribution; the mean and variance are equal.

8. Solve the following problem using Simplex method:

Minimise 2x1 15x2 5X3 6x4
subject to x1 6x2 3X3 x4 2
-2x1 5x2 X3 3x4 -3
xi, x2, x3, x4 Find dy/dx for y

(ii) Find dy/dx1 and dy/dx2 for y (2x1 (x2 2). Given 100 2P 0·02Y, where
Q= quantity demanded,
P price and Y income,
and given P 20 and Y 5,000, find the price elasticity and income elasticity of demand.

10. Assume that women and men exist in society in equal number. Given that of the men are colour blind and 0·025% of the women are colour blind, find the probability that a person drawn at random is colour blind. Also find the probability that having drawn a colour blind person, the person is a male.

11. Explain the Hawkins-Simon condition for the viability of an economy.

12. A company sold a commodity each year as shown in the table below <img src='./qimages/9912-12.jpg'> Find the y ax b. least square regression line Use the least square regression line as a model to estimate the sales of the company in 2012