LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.C.A. DEGREE EXAMINATION – COMPUTER APPLICATIONS
THIRD SEMESTER – APRIL 2008
CA 3201/ CA 3200 - (STATISTICAL METHODS)
Date : 05-05-08
Time : 1:00 - 4:00
Dept. No.
DC 4
Max. : 100 Marks
Section A
Answer ALL the questions.
10 × 2 = 20
,
1. Define quartiles.
2. Find the mode for the following distribution:
Class interval: 0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency : 5
8
7
12
28
20
10
3. State the properties of regression lines.
4. Define correlation coefficient.
5. Two unbiased dice are thrown. Find the probability that the total of the numbers on the dice is less than
five.
6. Prove that if A and B are independent events, then A and B are independent.
7. Write down the marginal density functions.
8. A coin is tossed until a head appears. What is the expectation of the number of tosses required?
9. Find the moment generating function of a uniform distribution.
10. Define Normal distribution.
Section B
Answer ALL the questions.
5 × 8 = 40
11. (a) An incomplete frequency distribution is given as follows:
Variable Frequency
10 – 20
12
20 – 30
30
30 – 40
?
40 – 50
65
50 – 60
?
60 – 70
25
70 – 80
18
Total
229
Given that the median is 46, determine the missing frequencies, using the median formula.
(OR)
(b) The first four moments of a distribution about the value 4 of the variable are -1.5, 17, -30 and 108.
Find the moments about mean, 1 ,
 2 . Find also the moments about origin.
12. (a) Find the coefficient of correlation for the following heights (in inches) of fathers (X) and their
sons(Y):
X
:
65
66
67
67
68
69
70
72
Y
:
67
68
65
68
72
72
69
71
(OR)
(b) A random sample of students of XYZ University was selected and asked their opinion about
‘autonomous colleges’. The results are given below. The same number of each sex was included within
each class-group. Test the hypothesis at 5% level that opinions are independent of the class groupings.
(Given value of chi-square for 2, 3 degree of freedom are 5.991, 7.82 respectively)
class
B.A/B.Sc part I
B.A/B.Sc part II
B.A/B.Sc part III
M.A/M.Sc.
Favouring ‘autonomous
colleges’
120
130
70
80
Opposed to
‘autonomous colleges’
80
70
30
20
1
13. (a) A and B throw alternatively a pair of balanced dice. A wins if he throws a sum of six points before
B throws a sum of seven points, while B wins if he throws a sum of seven points before A throws a sum
of six points. If A begins the game, show that his probability of winning is 30/61.
(OR)
(b) The odds that person X speaks the truth are 3 : 2 and the odds that person Y speaks the truth are 5
: 3. In what percentage of cases are they likely to contradict each other on an identical point?
14. (a) For the joint probability distributions of two random variables X and Y given below, calculate (i)
the marginal distributions of X and Y and (ii) conditional distribution of X given the value of Y=1 and
that of Y given the value of X=2.
X \ Y
1
2
3
4
1
4/36
1/36
5/36
1/36
2
3/36
3/36
1/36
2/36
3
2/36
3/36
1/36
1/36
4
1/36
2/36
1/36
5/36
(OR)
(b) Obtain the moment generating function of the random variable X having probability density function,
; 0  x 1
 x

f ( x)  2  x ; 1  x  2
 0
; elsewhere

15. (a) An insurance company insures 4,000 people against loss of both eyes in a car accident. Based on
previous data, the rates were computed on the assumption that on the average 10 persons in 1,00,00 will
have car accident each year that result in this type of injury. What is the probability that more than 3 of
the insured will collect on their policy in a given year?
(OR)
(b) Define an exponential distribution. Find the mean and variance of the same.
Section C
Answer any TWO questions:
2 × 20 = 40
16. (a) Calculate median for the following frequency distribution.
Class interval: 0-8
8-16 16-24 24-32 32-40 40-48
Frequency : 8
7
16
24
15
7
(b) In a partially destroyed laboratory, record of an analysis of correlation data, the following results only
are legible: Variance of X = 9. Regression equations: 8X -10Y + 66 = 0; 40X -18Y = 214 . What are:
(i) the mean values of X and Y, (ii) the correlation coefficient between X and Y, and (iii) the
standard deviation of Y?
(8+12)
17. (a) State and prove addition theorem of probability.
(b) The chances that doctor A will diagnose a disease X correctly is 60%. The chances that a patient will
die by his treatment after correct diagnosis is 40% and the chance of death by wrong diagnosis is
70%. A patient of doctor A, who had disease X, died. What is the chance that his disease was
diagnosed correctly?
(10+10)
18. (a) Two random variable X and Y have the following joint p.d.f.:
2  x  y ;0  x  1;0  y  1
f ( x, y )  
otherwise
 0
Find (i) Marginal p.d.f. of X and Y.
(ii) Conditional density functions.
(iii) Var(X) and Var(Y).
(iv) Covariance between X and Y.
(b) A and B play a game in which their chances of winning are in the ration 3:2. Find A’s chance of
winning at least three games out of the five games played. (14+6)
2