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Exam Details

2022 Statistics Paper - II

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Questions 80
Duration 180 mins
Package National Defence Academy and Naval Academy Examination (I) & (II) - Previous Year Papers

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Subject distribution

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Topic distribution

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Subtopic distribution

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Difficulty distribution

Medium 27 33.8%
Hard 27 33.8%
Easy 26 32.5%

Question type distribution

Multiple Choices 80 100%

Syllabus

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Sample questions from this paper

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1
2022 · Unclassified
2022 Statistics Paper - II
Let Y = Xβ + ε, where Y is n × 1 vector of response, X is n × k (n > k) matrix of predictors, β is k × 1 vector of unknown coefficients to be estimated and ε is n × 1 vector of random errors. Further ε is N(0, σ2I). The distribution of Ŷ is :
A
N(Xβ, σ2)
B
N(Xβ, X(X'X)−1 X' σ2)
C
N(Xβ, (X'X)−1 σ2)
D
N(Xβ, (X'X)−1 X' σ2)
2
2022 · Unclassified
2022 Statistics Paper - II
An ecologist takes data (Xi,Yi); i = 1, 2, 3, ... n where Xi is the size of an area and Yi is the number of moss plants in the area. We model the data by Yi ~ Poisson (θxi); Yi's are independent. The least square estimator and the MLE of θ are respectively : [IMAGE]
A
(∑i=1n Yi / ∑i=1n Xi , ∑i=1n Xi Yi / ∑i=1n Xi2 )
B
(∑i=1n Xi Yi / ∑i=1n Xi2 , ∑i=1n Yi / ∑i=1n Xi )
C
(Ȳ / X̄ , Cov(X, Y) / V(X))
D
(Cov(X, Y) / V(X) , Ȳ / X̄)
3
2022 · Unclassified
2022 Statistics Paper - II
Let A be any n × m matrix with A− as any generalized inverse of it. Further, let H = AA− and T = A− A. Then which one of the following is correct ?
A
Only H is an idempotent matrix
B
Only T is an idempotent matrix
C
Both H and T are idempotent matrices
D
Neither H nor T is an idempotent matrix
4
2022 · Unclassified
2022 Statistics Paper - II
Let A be a matrix of order n × p with A− as any generalized inverse of it. Let (A'A)− be any generalized inverse of A'A, then which of the following are correct ? 1. (A')− = (A−)' 2. A− = (A'A)− A' 3. Rank (A−A) = rank (AA−) Select the correct answer using the code given below :
A
1 and 2 only
B
2 and 3 only
C
1 and 3 only
D
1, 2 and 3
5
2022 · Unclassified
2022 Statistics Paper - II
Let A be any matrix of order n × m. Consider the following statements for its Moore-Penrose inverse A+ : 1. A+ = (A'A)+ A' 2. A+ is unique Which of the above statements is/are correct ?
A
1 only
B
2 only
C
Both 1 and 2
D
Neither 1 nor 2
6
2022 · Unclassified
2022 Statistics Paper - II
Let Xi, Yi and Zi; i = 1, 2, 3 be nine independent observations with common variance σ2, and E(Xi) = θ1, E(Yi) = θ2, E(Zi) = θ1 − θ2; i = 1, 2, 3. If θ̂1 and θ̂2 denote the BLUEs of θ1 and θ2 respectively, then which one of the following is correct ?
A
V(θ̂1) > V(θ̂2)
B
V(θ̂1) = V(θ̂2)
C
V(θ̂1) < V(θ̂2)
D
V(θ̂1) ≥ V(θ̂2)