| Post Name | LECTURER IN STATISTICS |
|---|---|
| Department | KERALA COLLEGIATEN EDUCATION |
| Question Paper Code | 122/2014 |
| Date of Test | 8 August 2014 |
| Medium of Question | ENGLISH |
| Exam Type | OMR Examination |
| Total Questions | 100 |
1
Which of the following statements is not correct ?
| 5
Answer
A. The family F consisting of all finite subsets of
2
Which of the following is a sufficient condition for the real valued function f to be Riemann
integrable with respect to « on
Answer
C. fis of bounded variation on
3
Which of the following sequences [{,} is not uniformly convergent on
Answer
D. f_n(x) = nx(1 - x^2)^n
4
Let A bea set of rational numbers in
Answer
B. 0
5
If [x] denotes the greatest integer function, then the value of the Riemann-Stieltjes
2
integral ["[x] d(x* ) is:
Answer
A. 3
6
The following vectors (1, 9, 9, 8), (2, 0, 0, 8), (2 0, 0, 3) are :
Answer
B. Linearly independent
7
Thematrix|_; 9 |'s@:
Answer
A. Hermitian matrix
8
If Aisa6x6 matrix of rank 4 then its nullity is ;
Answer
A. 2
9
What type of definiteness does the quadratic form x?+ 2y? + 322+ 2yz—2xz-+2xy possess ?
Answer
D. Indefinite
10
Identify the incorrect statement from the following:
Answer
D. The Moore–Penrose g-inverse is not unique
11
Which of the following doesn’t hold true always ?
Answer
D. P(Union from i=1 to n of A_i) <= 1 - Sum from i=1 to n of P(A_i^c)
12
If X > 0 a.s., then which of the following inequalities is wrong?
Answer
C. E(X^(1/2)) >= (E(X))^(1/2)
13
If X is a uniform [0, 1] random variable, then which of the following is a lower bound for P{|X - 1/2| <= 1/4}?
Answer
A. 8/9
14
Choose the correct statement:
Answer
B. Xₙ →ᵃ·ˢ X ⇒ Xₙ →ᴾ X
15
Let {X,} be a sequence of random variables with |
1 |
P(X, =n) = 7 P(X, =0)=1- of t>0_ Then,
Answer
A. X_n converges in probability to 0
16
If X is a non - negative random variable with distribution function F, then which of the
following represents E(X) ?
Answer
D. Integral from 0 to infinity of (1 - F(x)) dx
17
The probability that a contractor will get a plumbing contract Is 2/3 and the probability that
he will not get an electric contract is 5/9. If the probability of getting at least one contract is
4/5, what is the probability that he will get both contracts /
Answer
C. 14/45
18
Let {Xₙ} be a sequence of i.i.d. random variable with E(Xₙ²) < ∞. Let Sₙ = Σₖ₌₁ⁿ Xₖ, σ² = Var(Xₙ) > 0 and Z ~ N(0, 1). Then,
Answer
D. (Sₙ − E(Sₙ)) / √(nσ) →ᵈ Z
19
= pe pak: o’ =Var(X,) >Qg and Z~N
Answer
C. Jno?
20
Which type of convergence is used in central limit theorem ?
Answer
B. Convergence in r'h mean
|
21
If Pₓ(s) denote the p.g.f of the random variable X, then the p.g.f of Y = mX + n, where m, n are integers (m ≠ 0) is given by:
Answer
A. sⁿPₓ(sᵐ)
22
Let X and Y be independent standard normal random variables. Then the distribution of Z = ((X - Y)/(X + Y))^2 is:
Answer
D. F distribution with (1, 1) d.f.
23
Let X and Y be independent standard normal random variables. Then the distribution of
re =— Soe ; he 4
Xe pO
Answer
A. Chi - square distribution with 2 d.f
24
If rho_XY is the correlation between X and Y, then the correlation between U = a + cX and V = b - dY, where a, b, c, d > 0, is:
Answer
B. -rho_XY
25
In a partially destroyed laboratory record of an analysis of correlation data, only the regression equations 8x - 10y + 66 = 0 and 40x - 18y - 214 = 0 are legible. Then the mean value of Y is:
Answer
B. 17
26
If X ~ Poisson(lambda_1), Y ~ Poisson(lambda_2), and X and Y are independent, then the conditional distribution of X given X + Y is:
Answer
A. Binomial
27
If X~ Poisson (h,), Y~ Poisson(A,) and X and Y are independent, then the conditional
distribution of X given X + Y is:
Answer
C. Negative binomial
28
The distribution of X_(n) = Max(X_1, X_2, ..., X_n), where X_1, X_2, ..., X_n are i.i.d. beta(alpha, 1), is:
Answer
A. beta(alpha n, 1)
29
The distribution of X/,..=Max.
Answer
B. ,
30
If the moment generating function of X is M(t) = (2/5)e^t + (1/5)e^(2t) + (2/5)e^(3t), then its mean and variance are respectively:
Answer
C. 2 and 0.8
31
[If the moment generating function of X is M(t) = =e! + =o + se", then its mean and
variance are respectively :
Answer
D. land 05
122,/2014 6 A
32
Which of the following statements is not correct ?
Answer
A. if a sample of size n is drawn from a population of size N in such a way that every
possible sample of size ‘n’ has the same chance of being selected, the sample thus
‘ obtained is a simple random sample
33
With regard to ratio estimation based on the response variable y and subsidiary variable x,
identify the correct statement of the following -
Answer
D. The ratio estimation is usually superior to regression in estimation if the relationship
between the y 5 and x's is a straight line not through the origin
34
A sociologist wants to estimate the average income per adult male in a certain small city
where no list of resident adult is available. What would be the logical choice of the survey
design in this case ?
|
Answer
C. Stratified sampling
35
Which of the following statements is not correct ?
Answer
B. Systematic sampling often provides more information per unit cost than simple random
| sampling
36
A national survey of University student opinions 1s conducted by selecting a simple random
sample of universities from all those in the country and then selecting a simple random
sample of students from each university. What sort of sample survey design is used here ?
Answer
A. Stratified random sampling
37
Ina BIBD, four treatments are arranged in four blocks of three plots each. Each treatment
occurs once and only once in three blocks and any two treatments occur together in A blocks.
Then the value of A is:
Answer
D. 4
A 7 122/2014
(P.T.O.]
ne
38
Under a 2*-factorial design, what interaction is confounded with the following blocks ?
Block1; (1) ad ac ab cd bd be abed
Block 2: a ai -i¢ b acd abd abe bed
-
Answer
A. AB
39
Consider the linear model : .
y, = 0, +20, — 26, +e,
¥2= 8, +30, —0, +€5
Where y; are observations, 8, are parameters and e, are uncorrelated random variables with
mean zero and constant variance for i=1, 2, 3. Then which of the following is true ?
Answer
A. 24, =~ ¥, is an unbiased estimator of 0, —40,
40
In the ANOVA for an RBD with 4 blocks and 6 treatments having one missing value which
is estimated, the error degrees of freedom is :
|
Answer
B. 15
41
For which of the following set of values will a Balanced Incomplete Block Design of parameters
(v, b, r, k,
Answer
D. an F distribution with (m, n) d.f.
42
‘Test statistic for test the significance of difference between variance of two normal populations
with known means based on two independent samples of sizes m and respectively
follows :
Answer
A. an F distribution with (m—-1, a—1) dt.
43
If X,, X,.........¥, is a random sample from a normal distribution N(u, o) then the MLE of
o* when « is known is :
Answer
D. Neither consistent nor unbiased
44
If X1, X>, ........X, is a random sample from a population with density function
1 —ty-
f(x)= 3° | — 0 < x <, then the MLE of the parameter 0 is :
Answer
C. alpha <= beta
45
A test with size a and power f is said to be an unbiased test if :
Answer
C. asf
46
Tf Xy, Xp. பட ம be a random sample from N
Answer
B. . > x? is sufficient for 6
47
For an SPRT with strength
Answer
A. ,
48
the UMP critical region of size a for test the hypothesis Ho: 4=2 against Hy : u < 2 when
za is the ath quantile of a standard normal distribution is :
Answer
C. Sum X_i(n - Sum X_i)/(n(n - 1))
49
Let T be an ancillary statistic for the parameter θ. Then T and S are independent if:
Answer
A. S is complete sufficient for θ
50
Let T be an ancilliary statistic for the parameter 0- Then T and S are independent if :
Answer
D. Sis consistent for 6
51
If W is the Wilcoxon rank sum statistic and U is the Mann - Whiteny U statistic, then :
Answer
C. த
52
If X follows N,
Answer
B. Ais ofrankr
53
Let R be the sample correlation coefficient of
a bivariate sample of size n from a bivaraite
normal population with correlation coefficient p. If p=0 then the statistic Rp | — 2 follows
LR
Answer
D. F distribution
54
The distribution of Hotelling’s ‘I? statistic follows -
Answer
C. Wishart
55
Let X1, Xo) wou
a
|
distribution
Answer
C. Wo [F-
56
If {Nₜ, t ∈ T} is a Poisson process with rate λ then which of the following is/are correct: (a) Nₜ has independent increment (b) P(Nₜ₊ₕ − Nₜ = 1) = λt + O(h) (c) Nₜ is a stationary increment process
Answer
A. a, b and c
57
If {X_n, n = 0, 1, ...} is a Galton-Watson branching process with E(X_1) = m, then the probability of ultimate extinction is 1 if:
Answer
D. m <= 1
58
If {X,, n=0, 1,
probability of u
ing is/are correct :
N,=1)=At+0(h)
Answer
D. (a), (b) and (c)
59
Which of the following statement(s) is/are true? (a) The state space of a finite Markov chain contains at least one recurrent state. (b) In a finite irreducible Markov chain all states are non-null recurrent. (c) A null recurrent aperiodic state of a Markov chain is called ergodic.
Answer
A. (a) and (b)
60
Which of the following statement(s) is/are true ?
Answer
C. A null recurrent aperodic state of a Markov chain is called ergodic
61
Let X be a random variable which follows a Poisson distribution with parameter A and the
prior distribution of \ follows G(a,
Answer
B. then the posterior distribution is :
62
For the linear model Y = Xβ + ε, where ε is a vector of non-observable random variables with E(ε) = 0, then the least square estimate of β is:
Answer
B. (X′X)⁻¹X′Y
63
The hazard function of Weibull distribution with shape parameter β is monotone increasing when:
Answer
A. β > 1
64
Let T be a random variable with hazard function h(t) = a/t, 1 < t < infinity. Then the distribution function of T is:
Answer
B. 1 - 1/t^a
65
The hazard function of Wiebull distribution with shape parameter # is monotone increasing
when:
Answer
D. B>0
66
If p is the mean percent defective, then the upper control limit for the proportion defective is:
Answer
A. p + 3 sqrt(p(1 - p)/n)
67
Which distribution is used to find the probability of acceptance for an OC curve?
Answer
C. Binomial
68
Which source of variation can be estimated by the ratio-to-trend method?
Answer
D. Seasonal
69
The Bayesian point estimate is obtained by:
Answer
B. Minimising the expected loss
70
Which source of variation can be estimated by ratio-to-trend method ?
Answer
A. Cyelic
71
A good scientific research is characterized by:
Answer
D. All the above
72
To understand human behavior and reasons over a long period of time one has to do:
Answer
C. Longitudinal study
73
Teaching and learning arrangements, usually in small groups, that are structured to produce active participation in learning is:
Answer
D. Workshop
74
To understand human behavior and reasons over a long period of time one has to do :
Answer
C. Longitudinal study
75
Teaching and learning arrangements, usually in small groups, that are structured to produce
active participation in learning is :
Answer
D. Workshop
76
Directly useful application of scientific principles to production is called :
Answer
C. Technology
77
Which of the following qualities a researcher must have ?
Answer
D. All the above
78
The most effective teaching method that ensures maximum participation of students is ;
Answer
A. Lecture method
79
Which of the following can be achieved through value education ?
Answer
A. To inculcate of virtues
80
Teaching method where purposeful activity that will remove a recognized difficulty or
perplexity in situation through the process of reasoning is :
Answer
B. Problem solving method
81
_ _ of The Constitution of India directs the State to organize village panchayats an
endow them with powers and authority to function as units of self-governments.
Answer
B. Article 40
82
Article ———_oof The Constitution of India imposes a duty upon citizens to uphold and
protect the sovereignty, unity and integrity of Inclia.
Answer
C. 51-A(
83
All-India services can be created by The Parliament as empowered under ____ of The
Constitution of India.
Answer
A. Article 312
84
Freedom as to payment of taxes for promotion of any particular religion is guaranteed under
Article ___ of The Constitution of India.
Answer
B. 27
85
In Sodan Singh v New Delhi Municipality AIR 1989 SC 1988, The Supreme Court was called |
upon to decide whether ___
Answer
D. Hawkers had a fundamental right to carry on their trade on pavements meant for
pedestrians
86
First appeal under Section 19(1) of The Right to Information Act 2005 has to be preferred
| within _——__ days from the expiry of period for receipt of information or from date of
| decision.
Answer
B. thirty
87
As per Section 4(1)
Answer
D. ten
88
As per Section 22(1)
Answer
B. of The Transplantation of Human Organs Act 1994, no court shall
take cognizance of an offence except on complaint filed by a person who has given notice of |
not less than Ss days to the Appropriate Authority, of the alleged offence and his
intention to make the complaint. ,
89
As per Section 10(1) of The Scheduled Castes and Scheduled Tribes (Prevention of Atrocities)
Act 1989, a special court can pass an externment order against a person likely to commit
offence, and direct him not to return to the concerned area for such period not exceeding
__.___s as may be specified in the order. ‘
|
Answer
C. two years
90
According to Rule 2(j) of The Noise Pollution (Regulation and control) Rules 2000,
‘Night Time’ has been defined as the period between ss.
Answer
A. 10 pm and 6 am
91
Who was the founder of “Sadhu Jana Paripalana Sangham’ 7?
Answer
B. Ayyankali
|
92
The social organisation in Kerala, ‘Samathwa Samajam’ was established in the year :
|
Answer
A. 1836
93
Which among the following is not written by G. Sankara Kurup ?
Answer
D. Kunnimanikal
94
Author of the famous book “‘Jaathikkummi’ :
Answer
A. K.P. Karuppan
95
The Renaissance leader in Kerala, who got the name ‘Kumara Guru’ :
Answer
C. Poikayil Yohannan
96
The name given to the Airforce’s rescue operation provided to the flood victims
of Uttarakhand : |
Answer
B. Operation Rahat
|
97
Which year has formally declared by UN General Assembly as ‘International year of family
farming ?
Answer
A. 2014
98
The commission appointed for studying the contributory pension system in Kerala :
Answer
D. Bhattacharya Commission
99
Which Constitutional Amendment incorporated Panchayati Raj System in our
| constitution ?
Answer
C. 73'¢ Amendment
100
The nodal agency for estimation of poverty at the national and state level in India ;
Answer
B. Planning Commission
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