LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
FIFTH SEMESTER – APRIL 2011
ST 5505 – TESTING OF HYPOTHESES
Date : 18-04-2011 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
Exams Question Papers General Knowledge Election Directory
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
FIFTH SEMESTER – APRIL 2011
Date : 18-04-2011 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
SIXTH SEMESTER – APRIL 2011
Date : 09-04-2011 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
SECTION A (10 x 2 = 20 Marks )
Answer ALL the questions
= 10.2 , 12.1, 10.8 and 10.9
R = 1.1 , 1.3 , 0.9 and 0.8
A2= 0.73 ; D3 = 0 ; D4 = 2.28 ; d2 = 2.059
Find the control limits for chart.
SECTION B ( 5 x 8 = 40 Marks )
Answer any FIVE questions
SECTION C ( 2 x 20 = 40 Marks )
Answer any TWO questions
Stem and Leaf-plot by selecting the stem values 5, 6,7,8 and 9.
Week : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Yield : 58 63 69 72 51 79 83 86 85 78 87 83 64 73 81 68 72 65 91 88
Week: 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Yield : 64 68 67 60 59 63 64 52 70 92 75 76 81 74 82 76 75 62 63 92
deviation of 1.00. The product is presently being sold to two customers who have different
specification requirements. Customer A has established a specification of 48 4.0 for the
product, and customer B has specification of 46 4.0. Use normal distribution and find what
percentage of items go outside the specification limits of (i) Customer A, (ii) Customer B.
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
FIRST SEMESTER – APRIL 2011
Date : 06-04-2011 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
Section A Answer ALL the questions 10×2=20
Does this mean that event B is statistically independent of the event A?
if 0 £ x £ 1 and 0, otherwise, find the value of k. Hence find E (x).
E(X) £ E(Y) provided they exist.
Section B Answer any FIVE questions 5×8=40
follows a Poisson distribution with parameter, l. Hence find the mean and variance of X.
random. Find the probability that among the balls drawn, there is at least one ball of each colour.
B, P (AÈB) + P (AÇB) = P (A)+P (B)
From this vessel a ball is drawn and found to be white. What is the probability that, out of four
balls transferred, 3 were white and 1 was black?
that (i) coins are replaced before the second trial, (ii) the coins are not replaced before the
second trial. Find the probability that the first drawing will give 4 gold and the second 4 silver
coins.
cent are in sales. Of the employees who did not graduate from the college, eighty per cent are
in sales.
probability that an employee selected at random is neither in sales nor a college graduate?
favour of Manager Y settling the same dispute are 14:16. (a) What is the probability that
neither settles the dispute, if they both try independently of each other? (b) What is the
probability that the dispute will be solved?
0, otherwise, Use Chebyshev’s Inequality to obtain an upper bound for P [ |X –E(X) | > 2s ].
Compare it with the exact probability.
Section C Answer any TWO questions 2×20=40
(b) An Urn contains four tickets marked with numbers, 112, 121, 211, 222, and one ticket is
drawn at random. Let Ai (i=1, 2, 3, ) be the event that ith digit of the number of the ticket
drawn is 1. Discuss the mutual independence and pair-wise independence of the events.
(b) Suppose that Urn I contains 1 white, 2 black and 3 red balls. Urn II contains 2 white, I black
and 1 red balls. Urn III contains, 4 white, 5 black and 3 red balls. One Urn is chosen at
random and two balls are drawn from it. They happen to be white and red. What is the
probability that they have come from I, II or III?
(b) A petrol pump is supplied with petrol once in a day. If its daily volume of sales (X) (in
thousands of litres) is distributed by
f(x) = 5 (1-x) 4, if 0 £ x £ 1
What must the capacity be of is tank in order that the probability that its supply will get
exhausted in a given day shall be 0.01?
P (AÈB÷ C ) = P (A÷ C) + P (B÷ C) – P (AÇB÷ C)
and P (AÇBC÷ C ) + P (AÇB÷ C) = P (A÷ C).
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
SECOND SEMESTER – APRIL 2011
Date : 08-04-2011 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
PART – A
Answer ALL questions (10×2 =20 Marks)
PART – B
Answer any FIVE questions (5×8=40 Marks)
Find the marginal densities.
(a) (1, 2, 3), (2, 2, 0)
(b) (3, 1, -4), (2, 2, -3)
PART – C
Answer any TWO questions (2×20=40 Marks)
(b)Prove that the sequence given by is convergent.
(b) Find a suitable c of Rolle’s Theorem for the function
.
x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
P(x) |
0 | k | 2k | 2k | k2 | 2k2 | 7k2+k |
is the joint p.d.f. of X and Y, find the marginal p.d.f.’s. Also, evaluate
P[ (X < 1) (Y < 3) ]
(b) Find the rank of the matrix .
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
FIRST SEMESTER – APRIL 2011
Date : 19-04-2011 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
PART – A
Answer ALL questions 10×2=20
PART – B
Answer any FIVE questions. 5×8=40
Profit per shop: 0-10 10-20 20-30 30-40 40-50 50-60
No. of shops : 12 18 27 20 17 6
Year: 1994 1995 1996 1997 1998 1999
Production 7 9 12 15 18 23
Age of cars in years: 2 4 6 8
Maintenance cost
in Rs. Hundreds: 10 20 25 30
Passed Failed Total
Married 90 65 155
Unmarried 260 110 370
PART – C
Answer any TWO questions 2×20=40
Explain. (2+8)
Weekly wages: 10-15 15-20 20-25 25-30 30-35 35-40
No. of workers; 7 19 27 15 12 8 (7+3)
Class interval: 2-4 4-6 6-8 8-10
No. of person: 3 4 2 1 (3+5)
Marks: 1-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
No. of
persons: 10 25 20 15 10 35 25 10 (12)
(6)
Year ; 1978 1979 1980 1981 1982 1983
Price: 100 107 128 140 181 192 (14)
Boys Girls
No. of candidates appeared at an examination 800 200
Married 150 50
Married and successful 70 20
Unmarried and successful 550 110
Find the association between marital status and the success at the examination both for boys and girls. (10)
ST 5504 / ST 5500 ESTIMATION THOERY
Section A
Answer all the questions 10×2=20
1 Define an Unbiased Estimator.
Section B
Answer any five questions 5×8=40
(P.T.O)
13 Let X1,X2, ..Xn be a random sample taken from a population whose probability density function is
f(x, ) = exp{– }, >0, x>0
Use Factorization Theorem to obtain a sufficient statistic for .
T2(x) ={X1 +2X2+3X3}
T3(x) ={X1+X2 +X3+X4}
Examine their unbiasedness and compute their variances. Which one is the best estimator among the three? Find the efficiency of T1(x) and T2(x) with respect to T3(x).
(P.T.O)
Section C
Answer any two questions 2×20=40
19 (a) State and prove Chapman-Robbins inequality. Bring out its importance.
(b) Let X1,X2, ..Xn be a random sample taken from a normal population with unknown mean and unit variance. Obtain Cramer-Rao Lower bound for an unbiased estimator of the mean. (12 + 8)
(b) State and Prove Rao-Blackwell Theorem. (10 + 10)
(b) Show that Maximum Likelihood Estimator need not be unique with an example. Also, show that when MLE is unique, it is a function of the sufficient statistic. (10 + 10)
(b) State and prove a necessary and sufficient condition for a parametric function to be linearly estimable. (10 + 10)
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B. Ss. DEGREE EXAMINATION – STATISTICS SIXTH SEMESTER – April 2011 ST6604 / ST6601 – OPERATIONS RESEARCH Time: 3 hrs Max.:100 Marks |
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PART A
Answer ALL questions: (10 x 2 = 20)
PART B Answer any FIVE questions: (5 x 8 = 40)
Formulate this as a Linear Programming Problem.
Maximize z = x1 + 2x2 Subject to x1 + 2x2 £ 15 2x1 + x2 £ 20 x1 + x2 ³ 1 x1, x2 ³ 0
Find the optimal shipping schedule.
Player B
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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
FOURTH SEMESTER – APRIL 2011
Date : 07-04-2011 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
PART – A
Answer ALL Questions 10 x 2 =20
PART – B
Answer any FIVE Questions 5 x 8 =40
.
Compute the correlation coefficient of X and Y.
PART – C
Answer any TWO Questions 2 x 20 =40
Find .
(b) Derive the moment generating function of Negative binomial distribution.
conditional distribution of X given X+Y is binomial.
(b) Obtain the distribution of if X and Y are independent exponential variates with
parameter .
(b) Derive the moment generating function of chi-square distribution with n degrees of freedom
and hence find its mean and variance.
normal distribution. Also prove they are independently distributed.
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
SIXTH SEMESTER – APRIL 2011
Date : 05-04-2011 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
SECTION – A
Answer ALL the questions (10 X 2 = 20 Marks)
SECTION – B
Answer any FIVE questions (5 x 8 = 40 Marks)
SECTION – C
Answer any TWO questions (2 x 20 = 40 Marks)
variance.
examples.
observation is missing in the case of LSD.
and inference.
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
FIFTH SEMESTER – APRIL 2011
Date : 19-04-2011 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
SECTION – A
Answer ALL questions ( 10 x 2 = 20 Marks)
SECTION – B
Answer any FIVE questions. (5 X 8 = 40 Marks)
Year : 2000 2001 2002 2003 2004 2005
Chain index : 105 75 71 105 95 90
Month : jan feb mar apr may jun july aug sep oct nov dec
Seasonal index : 75 80 98 128 137 119 102 104 100 102 82 73
Age Standard population Population A
Population Specific Population Specific
(in ’000) death rate (in ’000) death rate
0 – 5 8 50 12 48
5 – 15 10 15 13 14
15 – 50 27 10 15 9
50 and above 5 60 10 59
SECTION – C
Answer any TWO questions. (2 X 20 = 40 Marks)
Year Item I Item II Item III Item IV
Price qty Price qty Price qty Price qty
2002 5.00 5 7.75 6 9.63 4 12.5 9
2005 6.50 7 8.80 10 7.75 6 12.75 9
Year : 1911 1921 1931 1941 1951 1961 1971
Population : 25 25.1 27.9 31.9 36.1 43.9 54.7
(in crores)
Fit an exponential trend y = abx and estimate the population in 2011.
x : 0 1 2 3 4 5 6
: 100 90 80 75 60 30 0
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
FIFTH SEMESTER – APRIL 2011
Date : 19-04-2011 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
SECTION – A
Answer ALL questions ( 10 x 2 = 20 Marks)
SECTION – B
Answer any FIVE questions. (5 X 8 = 40 Marks)
Year : 2000 2001 2002 2003 2004 2005
Chain index : 105 75 71 105 95 90
Month : jan feb mar apr may jun july aug sep oct nov dec
Seasonal index : 75 80 98 128 137 119 102 104 100 102 82 73
Age Standard population Population A
Population Specific Population Specific
(in ’000) death rate (in ’000) death rate
0 – 5 8 50 12 48
5 – 15 10 15 13 14
15 – 50 27 10 15 9
50 and above 5 60 10 59
SECTION – C
Answer any TWO questions. (2 X 20 = 40 Marks)
Year Item I Item II Item III Item IV
Price qty Price qty Price qty Price qty
2002 5.00 5 7.75 6 9.63 4 12.5 9
2005 6.50 7 8.80 10 7.75 6 12.75 9
Year : 1911 1921 1931 1941 1951 1961 1971
Population : 25 25.1 27.9 31.9 36.1 43.9 54.7
(in crores)
Fit an exponential trend y = abx and estimate the population in 2011.
x : 0 1 2 3 4 5 6
: 100 90 80 75 60 30 0