LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.C.A. DEGREE EXAMINATION – COMPUTER APPLICATIONS
THIRD SEMESTER – November 2008
CA 3201 / 3200/ 4200 - STATISTICAL METHODS
Date : 13-11-08
Time : 9:00 - 12:00
Dept. No.
PB 03
Max. : 100 Marks
PART A
(Answer ALL questions)
(10 x 2 = 20)
1. Find the arithmetic mean of the following frequency distribution:
x: 1 2 3 4 5 6 7
f : 5 9 12 17 14 10 6
2. Give the formula for Quartile Deviation.
3. State any two properties of Regression Coefficient.
4. Define consistency of data.
5. What is the chance that a leap year selected at random will contain 53 Sundays?
6. If A and B are independent events then prove that and are also independent.
7. Comment on the following: The mean of a binomial distribution is 3 and variance is 4.
8. Define Uniform distribution.
9. If E ( X )  2, E(Y )  5 . Find E (2 X  4Y ) .
10. A random variable X has the following probability function.
x
-2
-1
0
1
2
3
P(X = x) 0.1
k
0.2
2k
0.3
k
Find the value of k.
PART B
(Answer ALL questions)
(5x8=40)
11. (a) Calculate the mean for the following distribution:
class int erval : 0  8 8  16 16  24 24  32 32  40 40  48
.
frequency :
8
7
16
24
15
7
(OR)
(b) The average salary of male employees in a firm was Rs.5200 and that of females was Rs.4200.
The mean salary of all employees was Rs.5000. Find the percentage of male and female employees.
12. (a) Calculate the correlation coefficient 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) The demand for a particular spare part in a factory was found to vary from day –to-day. In a
sample study the following information was obtained:
Days : Mon Tues Wed Thurs Fri
Sat
No of parts demand : 1124 1125 1110 1120 1126 1115
The test hypothesis that the number of parts demanded does not depend on the day of the week.
(Given: the values of chi-square significance at 5,6,7 d.f. are respectively 11.07, 12.59, 14.07 at 5%
level of significance.)
1
13 (a) State and prove addition theorem of probability.
(OR)
(b) From a city population, the probability of selecting (i) a male or a smoker is 7/10,
(ii) a male smoker is 2/5, and (iii) a male, if a smoker is already selected is 2/3. Find
the probability of selecting (a) a non-smoker, (b) a male, and (c) a smoker, if a male
is first selected.
14 (a) A random variable X has the following probability function:
X
0
1
2
3
4
5
6
2
P(X=x) 0
k
2k
2k
3k
k
2k2
7
7k2+k
Find (i) k (ii) p(0<x<5) (iii) Determine the distribution function of X.
(OR)
(b) A random variable X is distributed at random between the values 0 and 1 so that its
probability density function is:
), where k is a constant. Find the
value of k. Using this value of k, find its mean and variance.
15. (a)With the usual notation find p for a binomial variate X, if n  6 and 9P  X  4  P  X  2
(OR)
(b) Find the moment generating function of an uniform distribution and hence find its
mean and variance.
Part C (Answer any TWO questions)
(2x20=40)
16. (a) Calculate: (i) Quartile Deviation(Q.D), and Mean Deviation (M.D) from mean for the
following data:
Marks : 0  10 10  20 20  30 30  40 40  50 50  60 60  70
No of students :
6
5
8
15
7
6
3
(b) Find the M.G.F of Poisson Distribution and hence find it’s Mean and Variance.
17. (a) In a partially destroyed laboratory record of an analysis of correlation data, the
following results only are legible: Variance of X = 9.
Regression equations: 8 X  10Y  66  0, 40 X  18Y  214. What are
(i) The mean values of X and Y (ii) the correlation coefficient between X and Y (iii) the
Standard deviation of Y?
(b) A and B throw alternatively with a pair of balanced dice. A wins if he throws a sum of
(10)
(10)
(10)
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.
(10)
18. (a) State and prove Baye’s theorem.
(8+12)
(b) Two random variables X and Y have the following joint probability density function:
. Find (i) Marginal density function of X
and Y (ii) Conditional density functions of X and Y (iii) Var(X), Var(Y) and
(iv) Covariance between X and Y.
*********************
2