LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
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M.A. DEGREE EXAMINATION – ECONOMICS
FIRST SEMESTER – APRIL 2007
EC 1809 – MATHS & STATISTICS FOR ECONOMISTS
Date & Time: 30/04/2007 / 1:00 – 4:00 Dept. No. Max. : 100 Marks
Part – A
Answer any FIVE questions in about 75 words each. (5 x 4 = 20 marks)
- Distinguish between partial and multiple correlation.
- Define ‘Multiple Regression’.
- Distinguish between secular trend and seasonal variation.
- Define ‘derivative’.
- State the conditions for maxima and minima in y = f(x)
- Define the distribution which explains improbable events.
- Find , if (i) (ii)
Part – B
Answer any FOUR questions in about 300 words each. (4 x 10 = 40 marks)
- State the properties of determinants.
- Find the output vector from the following input coefficient matrix and final demand vector
- Calculate Karl Pearson’s coefficient of correlation
X: 6 8 12 15 18 20 24 28 31
Y: 10 12 15 15 18 25 22 26 28
- Fit a straight line regression from the following data:
X: 0 1 2 3 4 5 6
Y: 2 1 3 2 4 3 5
- Define limit and continuity. Determine the right side limit and left side limit of the following functions and discuss the types of discontinuity.
(i) , (ii)
- Evaluate the following derivatives:
(i) (ii) (iii) ,
(iv) (v)
- Discuss the conditions of maxima and minima and saddle point form the function Z = f(x,y).
Part – C
Answer any TWO questions in about 900 words each. (2 x 20 = 40 marks)
- Derive the properties (Characteristics) of Cobb Douglas production function.
- Discuss the rules of differentiation with examples.
- Fit a Poison distribution to the following data:
No of mistakes per page: 0 1 2 3 4 5
No of pages: 40 30 20 15 10 5
- A normal distribution was fitted to the distribution of new business brought by 100 insurance agents with following results:
| New business (in ‘000 Rs) | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| Observed frequency | 10 | 20 | 33 | 22 | 15 |
| Expected frequency | 9 | 22 | 32 | 25 | 12 |
Test the goodness of fit.