EIJ-49869-A . 1. [Turn over
ROUGH WORK

1. Given 0.3, p and P(A.B) 0.58 then events A and B will be independent if p is
0.4 0.3
0 none of these
2. A problem in Statistics is given to 3 students whose chances of solving it independently are 11 1
and respectively, then the probability that the problem will be solved is
23 4
12


43
3

1
4
3. If 3 letters are to be put in 3 addressed envelopes, the probability that none of the letters are in the correct envelope is 1
0
6
11


3 2
4. If xi, i 3 are independently distributed as Uniform then the probability that exactly 1
2 of the 3 variables exceed is
3 P(B)12

33
24


9 9
5. For 2 events A and it is given that
P(AB)
P(AB)

Out of these

Only is correct Only is correct
Only is correct All the three are correct
6. In a binomial distribution mean variance 1 (mean)2 (variance)2 11
then p is
5

6
1 2

3 3
7. Let X has continuous distribution with cumulative distribution function then the distribution of Y is

Exponential Uniform


Normal None of these


8. The mean and variance of a random variable X are same then the distribution of X is

Binomial Poisson


Geometric Normal


9. Let X has Poisson distribution, with
P(x P(x
then the variance of x is


3 None of these
10. Let 3 and 13, then the Chebyshev's lower bound for x is
4
1
25
21
None of these
25
11. The probability that a non-leap year will have 53 Sundays is
1 2

7 7
5 6

7 7
12. If X and Y have the joint probability mass function
. 1 . x . 1 . y
c. ... y 2...
. 2 .. 3 .
then the value of c is
1 1

2 3

1
13. Let X has normal s2) distribution. If P[x 15] then µ is
2

10 15


20 None of these


14. Let the probability mass function of X be
. 3 .. 1 .
P(X ..... . x 3

. x .. 8 . 13
with moment generating function et)
8
3
mean
2
Out of these


Only is correct Only is correct


Both and are correct None is correct


t

15. If the moment generating function of X be then the variance of X is
t
1 1

2 3
1
None of these
12
16. If the joint pdf of be 0 y x 1
then the conditional expectation
E[Y X x is

2

2 2
1
None of these
x
17. Which one of the following distributions has memory less property

Normal Binomial


Exponential Uniform


18. A box contains white and black balls. balls are drawn without replacement. Then the
expected number of white balls drawn is
ac bc


a ba b
a

None of these
a b
19. For a negative binomial distribution

mean variance mean variance


mean variance not definite


20. Let X and Y are independent Poisson variates then the conditional distribution of X given is

Poisson Binomial


Geometric None of these


21. Let xand xbe independently binomially distributed as and respectively then
1 2 12
B(n1 n2, will be distribution of
n
1 2 122
x2 n1 x1 None of these
22. Let has bivariate normal 16, 25, then the conditional mean of Y given X 8 is

98

2
25
23. If x has exponential distribution with mean then P[x is
e-1
1- e-1
e-2
None of these
24. Let be a sequence of independent random variables with
P(X ± Ka) 1
K2
then Weak Law of Large Numbers (WLLN) holds if


1 1


a 1 None of these


2 2
EIJ-49869-A . 6.
n

22

25. If the pdf of normal N(µ s2) distribution be
2
3
x
ce 4 2
then s2) are None of these
26. The mean of first n natural numbers is
2

None of these
27. The mean weight of boys in a class is 60 kg and that of girls is 40 kg. If the average weight of the class be 46 kg, then the percentage of boys and girls in the class is

40) 60)


70) 30)


28. The sum of absolute deviations is least when measured from

mean median


mode geometric mean


29. A student pedals from his home to the college at the speed of 10 km/hour and back at the speed of 15 km/hour. Then his average speed in km/hour is

12 12.2


12.5 None of these


30. The harmonic mean of two numbers is 4 and their arithmetic mean and geometric mean

satisfy 2A G2 27, then the numbers are








31. In a moderately asymmetric distribution the median and mean are respectively 42 and 40, then the mode is

40 42


44 46


32. The relation between arithmetic mean geometric mean and harmonic mean is

A H G A G H


G A H H G A


33. Let X be a random variable with mean µ and median m then E(x b)2 is least if

b 0 b m


b µ None of these


34. A discrete random variable takes values and 1 with respective probability p and q. If 3
then the standard deviation of X is
5
4 16


5 25
4

None of these
5
35. The first 4 moments about a number are 10, 45, then the mean and variance are




None of these


36. If the possible values of X are 3.... then is
P(X P(X
8 8
.P(X .P(X
n=1 n=1
37. If two regression lines be 3x 5y 8 2x 5y 7
then the correlation coefficient between is

2
2

3 3

2
0
3
38. The means and variances of two independent random variables X and Y are same, then the
correlation between X is
1

0
2


1 1
2
39. If b and b be two regression coefficients and if b then
xy yx xy
b 1
yx yx
byx 0 not definite
EIJ-49869-A . 8.
40. If correlation between be 0.4, then correlation between -2X 3Y will be

0.4 0.4


0.0 1.0


41. For a .2-distribution

mean variance 2 mean variance


mean 2 variance none of these


42. If X has uniform distribution, then the pdf of the rth order statistic is

Exponential Beta


Uniform None of these


43. In a frequency distribution, the fourth central moment is double of the [variance]2 then the distribution is

Leptokurtic Platykurtic


Mesokurtic All of these


1
44. Let x has distribution, then the distribution of will be
x




.2 t


45. Let x has t-distribution with n degrees of freedom. If n then the distribution of t reduces to

Normal Cauchy


F None of these


46. The pdf of the first order statistic in 1e x x 0 is
.

Exponential Uniform


Beta None of these


47. The mean of first order statistic in Uniform 1 0 x 1
is
11


nn
1n


2
n n1

48. If for two attributes A and B
ß

independent


negatively associated


49. If the regression line of Y on X be
y ax b
then a is

s
. y

sx
.
where

then A and B are

positively associated


no conclusion


sx
.

sy
None of these
50. If range of correlation coefficient be then the correlation is

Partial


Rank


51. An unbiased estimator of . in .

Sample mean


Largest observation



Multiple


Simple


1 is
.

Sample median


Double of the sample mean


52. Sufficient statistic of . in . e x . is

min(x1,...., xn) max(x1,...., xn)


sample mean sample median


53. The minimum variance unbiased estimator (mvue) of .2 in normal distribution is 11
2 2

n n
x 2 None of these
54. Maximum likelihood estimator of s2 in normal s2) distribution when µ is unknown is
1 . n (xi x)2
n -11
1n2 1n2
. x .(xi
i
n n
1 1
55. If x1, x2 and x3 are independently distributed with mean then
T x1 2x2 .x3
is unbiased estimator of . if . is



56. Cramer-Rao Lower Bound (CRLB) for the variance of an unbiased estimator . from Poisson is
.

n
.
57. Maximum likelihood estimator of . in

1e x
2
is


Sample mean


Min


.2

n

.2


Max xn)


Sample median


58. Confidence interval for s2 in normal s2) distribution is based on the distribution

t normal


.2 F


59. Let X has Poisson distribution, then mle of e-. is
nxeX(n) xe x None of these
60. The mvue of . in
.x0, . 1 is
2X
1n X(n)1n n
where max Xn)
61. Which of the following statements is not true consistency does not imply unbiasedness unbiasedness does not imply consistency mle is function of sufficient statistic mle is unbiased

62. The moment estimator of s2 in normal s2) distribution, when µ is unknown is
1n2 1n2
.(xi .(xi
n1 n -11
1n 2
. xi none of these
n
1
63. For the pdf
1
0 x .
.
the moment estimator of . is


x


none of these


64. Let x1, x2 be a random sample of size 2 from the distribution
. 0 x 1
then sufficient statistic for . is

x x
12 1 2
x
x1 x2 1
x
2
65. MLE are always

unbiased unique


consistent none of these


66. Neyman-Pearson lemma is used for finding Most Powerful test for

Simple Vs simple hypotheses


Composite Vs simple hypotheses


67. For an exponential distribution
1e
. x . 0
.
the hypothesis to be tested is H0 . 1 H1 . 2

Simple Vs composite hypotheses


Composite Vs composite hypotheses


If on the basis of a single observation critical region be x 4 then the size of the test is

e2 1-e4


e2 e4


68. If n is the sample size, µ is the population mean and s2 is the population variance, then the standard error of sample mean is

s s/n

s
n s/2n


69. Let X has normal distribution where both µ ands2 are unknown. Then the simple hypothesis is

H0 s 5 H0 µ 10


H0 µ s H0 µ s 1


70. Which of the following is not related to probability of Type I error

a ß


level of significance size of the test


71. The number of runs in XYY X Y X X is


72. The expected value of the runs in Question 71 is

3.1 4


4.4 5.2


73. Let
X 10, 12, 7
Y 13, 15
then the value of Wilcoxon-Mann-Whitney statistic is



74. The distribution of statistic used in sign test is

Binomial Poisson


.2 t


75. The distribution of the statistic used in median test is

.2 t


F Binomial


76. In a simple random sampling without replacement (SRSWOR), the probability of a sample of size n drawn from
N units is
1n


N N
.. .

1

.. .

1


n
N

.

n
.

77. In SRSWOR, the variance of the sampling mean y Var( y in usual notation is
f
11

.. .

.. .

.. .

.. .

S2


S2




N

nN




.. .

N

n
.. .

.. .

1

f
.. .

S2


S2


N

n
78. The relation between variances in usual notation is
V V V
opt prop SRS opt SRS prop
V V
prop opt SRS SRS prop opt
79. A population consisting of 100 units is divided into two strata, such that N1 60, N2 40, 2 and 3. If by Neyman allocation 12, then the sample size n will be
1 2 1

24 12


6 none of these


80. The coefficient of variation in a large population is 10%. In order that the CV of the sample mean be the size of the simple random sample be
(B)10
25 250
81. In a SRSWOR, if y n 100, N 500 then the estimated population total is

250 500


2500 25000


82. In simple random sampling the relation between sampling fraction and finite population correction is

fpc f fpc 1 f


fpc None of these


83. If the variance of sample mean in SRS with and without replacement be V and V respectively
WRWOR
and e is
VWOR
e then the value of e is
VWR
N n

N N

N n
84. In a SRSWR from a population of 400 units, the finite population correction is 0.75, then the sample size is

100 75


60 50


85. If a population consists of a linear trend, then which of the following is correct

Var(yst =Var(ysys



where st Stratified, sys Systematic and R simple random sampling.



86. Under SRSWOR, n units are drawn from N units. If the ratio estimator of the population mean
Y¯ be
then is
.. .

.. .


Y

cov y



xcov x
.. .

.. .
.. .
.. .

y y


cov


cov
y
x x
.. .sys
87. The variance of the stratified sample meanRst sysRst is
Va
r(y
yst.))
Va
r

yy

Va
r

yy
st
E. X
. .
yR xL L
. yR . . 11 . 22 . 11 . 22
. . WS . . WS
...h n ...hn
N n nN
h=1 . hh . h=1 . hh .
L . 11 . 2
. . WS
..nN .h n None of these h=1 . hh .
L
L Nh
where N n ni, Wh .
1N

1
88. Basic principle of an experimental design is

Replication


Randomization


Local control
Out of these


Only is true Only and are true


Only and are true All and are true


89. In a m2 LSD, the degree of freedom of error is

m2 1 1)2


None of these


90. In a RBD with 5 treatments and 4 blocks, one observation is missing, therefore in ANOVA table, degree of freedom for error will be

12 11


10 None of these


91. In a m2 LSD, if the degree of freedom of treatment and error are same, then the value of m is


92. The estimate of the missing value in the following RBD
Treat. 1 Bl2 ock 3 4 Total
1 6 5 7 8 26
2 7 X 4 5 16 X
3 8 6 5 9 28
Total 21 11+X 16 22 70 X

is

3.6 4.1


5.5 7.8


93. In a LSD, relation between no. of replicates and no. of treatments is

r t r t


r t all of these


94. In a RBD, local control is used in K directions, where K is


95. The interaction effect in a 2-way design can not be studied if the number of observations per cell is


96. A 23-experimental design is arranged in 2 blocks. If the principal block contains treatment combinations
ab, abc
then the confounded interaction is


AB AC


BC ABC


EIJ-49869-A . 16.
97. The number of confounded interactions in a 2n-experimental design arranged in 2k blocks is

2n k 2n-k 3


2k none of these


98. A two-way classification with m observations per cell has r rows and c columns. The degree of freedom for interaction in ANOVA table is

m 1





99. Local control is completely absent in

CRD RBD


LSD none of these


100. A m2-LSD is based on incomplete 3-way experimental design because the no. of experimental units are

m3 m4
ROUGH WORK

ROUGH WORK