In a country as vast and diverse as India, reliable data is the backbone of effective governance and policy-making. The Statistical System of India plays a crucial role in collecting, processing, analyzing, and disseminating data related to economic, social, and demographic aspects of the nation. From GDP estimation to employment statistics, the system ensures that decisions are based on scientific evidence rather than assumptions.

In a data-driven world, reliable and authentic data plays a crucial role in policy-making, research, and economic planning. India has a well-structured statistical system supported by various government institutions that generate official data across sectors like population, economy, labor , and development.

Changing Scenario of Pulses Cultivation and Production in India

Which of the following statements are correct in order to obtain the hypothesis H0:β1=0H_0: \beta_1 = 0H0​:β1​=0 for the modelyi=β0+β1xi+εiy_i = \beta_0 + \beta_1 x_i + \varepsilon_iyi​=β0​+β1​xi​+εi​ ?

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For a simple linear regression modely=β0+β1x+εy = \beta_0 + \beta_1 x + \varepsilony=β0​+β1​x+ε,consider the following statements where β^0\hat{\beta}_0β^​0​ and β^1\hat{\beta}_1β^​1​ are estimates of β0\beta_0β0​ and β1\beta_1β1​:

Let XXX be a random variable with probability generating functionP(s)=∑kpkskP(s) = \sum_{k} p_k s^kP(s)=∑k​pk​sk. Find the probability generating function of Y=2XY = 2XY=2X.

Question Let XXX be a Poisson variate with parameter λ\lambdaλ such that P(X = 2) = 2P(X = 4) + 20P(X = 6) What is the coefficient of skewness? Options: (a) 1/√3(b) 1(c) 1/2(d) −1/√3

Question:Which of the following statements are associated with residuals of a regression model? The sum of the residuals in any regression model that contains an intercept is always zero. The sum of the observed values yiy_iyi​ is not equal to the sum of the fitted values y^i\hat{y}_iy^​i​. The sum of the residuals weighted by the corresponding regressor variable is zero. The sum of the residuals weighted by the corresponding fitted values is zero. Select the c

Question What are Western Disturbances and Westerlies, and how are they different from monsoons? In which part of India are they mainly confined? ISS PREVIOUS YEAR GS 2016 Q.NO. 2(b)

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Let the random variable X have the distribution: P(X = 0) = P(X = 3) = p P(X = 1) = 1 − 3p P(X = 2) = p where 0 ≤ p ≤ 1/2 Find the maximum value of V(X).

Which of the following statements are correct about the generalized inverse of a matrix A? A generalized inverse of a matrix is defined as A A⁻ A = A A generalized inverse is not unique. A matrix to have a generalized inverse must be non-singular. A matrix to have a generalized inverse may be either a square matrix or a rectangular matrix. Select the correct answer using the code given below:

What is Polar Shifting? Discuss its geographic significance with regard to catastrophic consequences on humanity.

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ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION SET-A ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION SET-A Random Effects Model Question (ISS Level) Question Suppose b₁, b₂, b₃, …, bₙ are independent N(0, σ²) random variables and eᵢⱼ are independent N(0, τ²) random variables for i = 1, 2, 3, …, k and j = 1, 2, 3, …, n. Suppose we observe only: Xᵢⱼ = bᵢ + eᵢⱼ for i = 1, 2, 3, …, k and j = 1, 2, 3, …, n. Then which of the following assertions are true? Var(Xᵢⱼ) = σ² + τ² for all i, j Cov(Xᵢ

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A Poisson random variable X has mean equal to 1/2. Let Y = 2X. Consider the following: E(Y) = 1 Var(Y) = 4 μ3(Y) = 4 μ4(Y) = 28 Which of the above is/are correct?

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