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2019 Statistics Paper - II
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80
Duration
180 mins
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National Defence Academy and Naval Academy Examination (I) & (II) - Previous Year Papers
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80questions
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80questions
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2019 · Unclassified
2019 Statistics Paper - II
If y1, y2, y3 and y4 are independent with E(y1) = E(y2) = (θ1 + θ2), E(y3) = E(y4) = (θ1 + θ3), and V(yi) = σ2, i = 1, 2, 3 and 4. For estimability of parametric function l'θ = l1θ1 + l2θ2 + l3θ3, consider the following conditions :
1. l1 = l2 + l3
2. l2 = l1 + l3
3. l3 = l1 + l2
Which of the above condition(s) is/are correct ?
2019 · Unclassified
2019 Statistics Paper - II
Let an n × 1 vector y ~ N(Xβ, σ2I) where X is an n × p matrix. Let H = (hij) = X(X' X)−1 X' be an n × n matrix. Let e = y - ŷ; ŷ = Xβ̂ be the n × 1 residual vector where β̂ is the least squares estimate of β. Then which one of the following is not correct ?
2019 · Unclassified
2019 Statistics Paper - II
For n observations (x1, y1), (x2, y2), ...., (xn, yn) two models were fitted.
1. yi = α + βxi + error; i = 1, 2, ..., n
2. yi = α + βxi + γxi2 + error; i = 1, 2, ..., n
Let ŷi and ŷi* be the estimated values of yi from the two models and if E = ∑i=1n (yi - ŷi)2 and E* = ∑i=1n (yi - ŷi*)2, then which one of the following is correct ?
2019 · Unclassified
2019 Statistics Paper - II
Let Y1, Y2, Y3 and Y4 be uncorrelated observations. It is given that
1. E(Y1) = β1 + β2 + β3 = E(Y2)
E(Y3) = β1 - β2 = E(Y4)
2. V(Yi) = σ2; i = 1, 2, 3, 4
Define e1 = 1/√2 (Y1 - Y2) and e2 = 1/√2 (Y3 - Y4). Then an unbiased estimator of σ2 is given by
2019 · Unclassified
2019 Statistics Paper - II
Consider the following ANOVA table :
The values of w, x, y and z that complete the above table are respectively
| Source of variation | Degrees of freedom | Sum of squares | Mean SS | Test statistic |
|---|---|---|---|---|
| Treatment | w | x | y | 5·22 |
| Error | 12 | z | 25 | |
| Total | 14 | 561 |
2019 · Unclassified
2019 Statistics Paper - II
For estimating the mode of a normal distribution, which one of the following is the most efficient estimator ?