# Loyola College B.A. Economics April 2008 Econometrics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.A. DEGREE EXAMINATION – ECONOMICS

# NO 16

FOURTH SEMESTER – APRIL 2008

# ST 4207 / 4204 – ECONOMETRICS

Date : 25/04/2008                Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION- A

Answer all the questions. Each carries TWO marks.                  (10 x 2 =  20 marks)

1. Define sample space and event of a random experiment.
2. If P(A) = ¼  , P(B) = ½  and P(AB) = 1/6 , find (i) P(AB) and (ii) P(AcB).
3. Given:

X= x :    0      1        2        3        4

P(X=x): 1/6  1/8     ¼      1/12    3/8

Find E(2X + 11).

1. If  f ( x, y) is the joint p.d.f. of X and Y, write the marginals and conditional

distributions.

1. Write any two properties of expected values.
2. Define BLUE.
3. Define the population regression coefficient .
4. Write variance inflating factor of an estimator in the presence of multicollinearity.
5. Define autocorrelation.
6. Define point and interval estimation.

SECTION –B

Answer any FIVE questions. Each carries EIGHT marks.                (5 x 8 =  40 marks)

1. Consider 3 urns. Urn I contains 3 white and 4 red , Urn II contains 5 white and 4 red and  Urn III contains 4 white and 4 red balls. One ball was drawn from each urn. Find the probability that  the sample will contain 2 white and 1 red balls.
2. If a fair coin is tossed 10 times, find the chance of getting (i) exactly 4 heads

1. Derive the least square estimators of the linear model  Y = 1  + 2 X + u .
2. State any six assumptions of the linear regression model.
3. How to fit a non-linear regression model of the form Y = 1 + 2 X + 3 X 2 ?.
4. Consider the model Y = 1  + 2 X + u  where X and Y denote respectively

consumer income (hundreds of dollars per person) and consumption of purple

oongs (pounds per person) . The sample size is 20 , sum of X is 300, sum of Y

is 120 , sum of squares of deviations of X from its mean is 500 , sum of product

of deviations of X and Y from their respective means is 66. 5 and sum of squares

of is 3.6.

• Compute the slope and intercept.
• Compute the standard error of regression.
• Compute the standard error of slope.

1. In a book of 520 pages , 390 typo- graphical errors occured. Assuming Poisson

law  for the number of errors per page, find the probability that a random sample

of 5 pages contain (i) no error (ii) atleast 3 errors.

1. The mean yield for one-acre plot is 662 kg with a standard deviation of 32 kg.

Assuming normal distribution find how many one-acre plots in a batch of 1000

plots will have yield (i) over 700 kg  (ii) below 65 kg .

SECTION – C

Answer any TWO questions. Each carries TWENTY marks.          (2 x 20 =  40 marks)

1. Consider the following joint distribution of (X,Y):

X          0            1            2               3

0        1/27      3/27       3/27           1/27

Y      1        3/27      6/27       3/27              0

2        3/27      3/27        0                  0

3        1/27        0           0                  0

(a) Find the marginal distributions of X and Y.

(b) Find E( X ) and V ( X )

(c) Find the correlation between X and Y.

(d) Find E ( Y | X = 2 )

(e) Verify whether or not X and Y are independent.

1. (a) Explain the following methods of estimation used in the analysis of regression

models:

(i) Maximum likelihood      (ii) Moments

(b) The heights of 10 males of a given locality are found to be 70 , 67, 62 , 68 , 61

68 ,70 , 64 , 64 , 66 inches. Is it reasonable to believe that the average height is

greater than 64 inches ? Test at 5% significance level.

1. For the following data on consumption expenditure (Y ) , income ( X2 ) and wealth

( X3 ):

Y(\$)   : 70     65      90       95      110      115     120     140      155       150

X2 (\$) : 80    100    120     140    160      180      200     220      240       260

X3 (\$) : 810  1009  1273   1425  1633    1876    2052   2201    2435     2686

• Fit a regression model Y = 2 X2 + 3 X3 + u .
• Find the correlation coefficients between Y and X2 , Y and X3 , X2 and X3.
• Test H0 : 2 = 3 = 0 at 5% significance level .

1. (a) For the k-variate regression model Y = 1 + 2 X2 +…+k Xk + u

carry out the procedure for testing  H0 : 2 = 3 = … =  k = 0 against

H1: atleast one k 0.

(b) Write the properties of ordinary least square(OLS) estimators under the

normality assumption.

Go To Main Page

Latest Govt Job & Exam Updates:

# View Full List ...

© Copyright Entrance India - Engineering and Medical Entrance Exams in India | Website Maintained by Firewall Firm - IT Monteur