In a steel factory, on an average, there are 6 defects per 10 square feet of steel sheet produced. If we assume a poisson distribution, what is the probability that and 18 square feet of steel sheet will have at least 7 defects?

Enlist the properties of a binomial distribution. Find the probability of getting 8 heads and 5 tails in 13 tosses of an unbiased coin

A good estimator should satisfy certain criteria. Discuss these criteria with illustration.

Under the simple regression analysis there are different methods of estimation. One of them is the Ordinary Least Square (OLS) method of estimation. Explain this method in detail.

We can derive some fundamental distributions with the help of Normal distribution. Enlist these fundamental distributions and explain each one of them in detail.

Discuss the properties of determinants. Use examples to elaborate your response.

“Analysis of economic relationships often requires inclusion of a large number of interrelated variables into the model. Linear algebra provides tools of solving simultaneous equations with the aid of matrices and determinants means for their concise presentation and solution mechanism”. In the light of this statement, explain the concept of matrix and determinants.

)Probability distribution function

Right-hand limit and left-hand limit

Algebraic function and Non-Algebraic function

What do you understand by constrained optimisation? Let the utility function be U (X, Y) = X2 + Y. Price of commodity X is Px = 2 and price of commodity Y is Py = 1. The income is M = 200. Find out the equilibrium quantities of X and Y, given the constraint M = PxX+ PyY.

What is a total differential? Find out the total differential of: f (x1 , x2 ) = 10x1 + x2 4 + 2bx1x2 + 5x2

What is a cross partial derivative? Find the cross partial derivative of: f (x1 , x2 ) = 4x3 + x2 4 + 3x1 3x2 4 + 5x1 x2

What is a partial derivative? Find the partial derivative of: f (x1 , x2 ) = 4x1 + 5x1x2 + 2x2

Under perfect competition, there is a firm producing two products. Quantity of first product is q1 and quantity of second product is q2 . Prices of both commodities must be taken as exogenous. The price of first product is given by p1 = 5 and the price of second product is given by p2 = 3. The firm’s cost function is assumed to be C = 2q1 2 + 2q2 2 + q1q2. Find out the following:

a) firm’s revenue function

b) firm’s marginal cost function for first product

c) firm’s marginal cost function for second product

d) firm’s profit function

e) the value of q1 and q2 that maximise the firm’s profits

f) Value of Hessian matrix

Explain any two economic applications of Definite Integral. Use examples to illustrate the applications.

f(x) = x3 + x2 + x + 1

f(x) = 3x3 + 4

If the second derivative is zero at a point, the function may have a maximum, a minimum or a point of inflexion. In the light of this statement, explain a maximum, a minimum and point of inflexion.

Constant Elasticity Demand Curve