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Exam Details

2025 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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Difficulty distribution

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

Question type distribution

Multiple Choices 80 100%

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Sample questions from this paper

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1
2025 · Unclassified
2025 Statistics Paper - II
Consider the following statements : I. MLEs are unbiased but not necessarily unique. II. Unbiased estimator is always unique. III. If U and W are consistent estimators of θ1 and θ2, then UW is also consistent for θ1θ2. Which of the statements given above is/are correct ?
A
I and II
B
I and III
C
II and III
D
III only
2
2025 · Unclassified
2025 Statistics Paper - II
With the increase in sample size if the estimator becomes closer and closer to the parameter, then it is called :
A
Completeness
B
Consistent
C
Sufficient
D
Unbiasedness
3
2025 · Unclassified
2025 Statistics Paper - II
Let X1, X2, X3, ..., Xn ~ N(μ, σ2) where mean μ and variance σ2 are unknown. Let S2 = (1/n) Σ(Xi - X̄)2 and s2 = (1/(n-1)) Σ(Xi - X̄)2. Which one of the following is correct according to the efficiency criterion ?
A
s2 is more efficient than S2.
B
s2 is less efficient than S2.
C
s2 and S2 cannot be compared.
D
Efficiency of s2 is equal to efficiency of S2.
4
2025 · Unclassified
2025 Statistics Paper - II
Suppose X1, X2, X3, ..., Xn be a random sample of size n from Poisson distribution with parameter λ. Then uniformly minimum variance unbiased estimator (UMVUE) of λ is :
A
(Σi=1n Xi2) / n
B
(Σi=1n Xi) / (n + 1)
C
(Σi=1n Xi) / n
D
(Σi=1n Xi2) / (n + 1)
5
2025 · Unclassified
2025 Statistics Paper - II
Let S be the set of all unbiased estimators T of θ ∈ Θ such that EθT2 < ∞ for all θ ∈ Θ. An estimator T0 ∈ S is called a uniformly minimum variance unbiased estimator (UMVUE) of θ for T ∈ S if :
A
Eθ(T0 - θ) ≤ Eθ(T - θ)
B
Eθ(T0 - θ)2 > Eθ(T - θ)2
C
Eθ(T0 - θ)2 ≤ Eθ(T - θ)2
D
Eθ(T0 - θ) > Eθ(T - θ)
6
2025 · Unclassified
2025 Statistics Paper - II
Let X1, X2, X3, ..., Xn be a random sample from N(μ, σ2). Consider the statistic s2 = (1/(n-1)) Σi=1n (Xi - X̄)2. What is V(s2) equal to ?
A
(2σ4) / (n - 1)
B
(2σ2) / (n - 2)
C
(2σ2) / (n - 1)
D
(2σ) / (n - 1)