Madras University (UnOM) 2006 M.C.A Computer Aplications Statistical Methods - Question Paper

Time: 3 hours
Maximum: 75 marks

Use of Statistical table is allowed.

PART A - [5 x five = Marks 25]
ans ALL ques..
All ques. carry equal marks.

1. (a) When 2 events are stated to be independent? provide an example.

Or

(b) obtain E (X) and E (X - Xbar)2 for the subsequent probability distribution

X -10 -20 30
P (X) 1/5 3/10 1/2

2. (a) Write a note on Binomial distribution.

Or

(b) In a normal population, 31% of the items are under 45 and eight percent are above 64. obtain the mean and standard deviation.

3. (a) Fit a straight line from the data provided beneath

X one two three four 5
Y -3 one five nine 13

Or

(b) obtain the rank correlation ranging from X & Y where

X 12 13 18 nine 10 11
Y seven nine five six eight 12

4. (a) define systematic sampling.

Or

(b) define the properties of a good estimator.

5. (a) discuss the use of 2 way classification.

Or

(b) Write a note on seasonal variations in time series.

PART B - [5 x 10 = Marks 50]
ans any 5 ques..
All ques. carry equal marks.

6. Let X be a continuous random variable with
probability distribution function
f(x) = ax, 0 <= x <= 1
f(x) = a, one < x <= 2
f(x) = -ax + 3a, 2< x <= 3
f(x) = 0, elsewhere

(a) Determine the constant 'a'.

(b) calculate P (X < = 1.5).

7. If X is the number scored in a throw of a fair die, show that the Chebyshev's inequality provide P [ |X -u | > 2.51 < 0.47 where u is the mean of X, while the true probability is zero.

8. 7 coins are tossed and number of heads noted. The experiment is repeated 128 times and the subsequent is obtained:

No. of heads 0 one two three four five six seven Total
Frequencies seven six 19 35 30 23 seven one 128

Fit a Binomial distribution assuming that the coin is unbiased.

9. The mean yield for one-acre plot is 662 kilos with a standard deviation 32 kilos. Assuming normal distribution, how many one-acre plots in a batch of 1,000 plots would you expect to have yield (a) over 700 kilos (b) beneath 650 kilos and Cc) what is the least yield of the best 100 plots?

10. In a trivariate distribution o1, = 2, o2 = three = 3, r12 = 0.7, r23 = r3l = 0.5. obtain

(a) r23.1 (b) R1.23 Cc) b12.3

provided Var W = nine

Regression equations : 8x - 10y = -66 and 40x - 18y = 214

obtain (a) the mean values of x and y (b) the correlation coefficient ranging from x and y (c) the standard deviation of y.

12. In a random sample of 500 men from a particular area of Tamil nadu, 300 are obtained to be smokers. In a different random sample of 1000 men from a different area, 500 are obtained to be smokers. Do the data indicate that the 2 areas are significantly various with respect to the habit of smoking.

13. The subsequent outcomes were found in 4 independent samplings. Perform the 1 way classification for analysis of variance.

(a) six 14 12 six two 5
(b) 10 17 six 19 19 16
(c) 11 11 19 23 eight 17
(d) 19 two 29 1614 20

Earning:   Approval pending.