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​:

Discuss the impact of Information Technology in the Industrial Revolution of India.

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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ISS PREVIOUS YEAR GS 2016 Q.NO. 5 What does Yoga represent in Indian philosophical tradition? Is it the same as that practised by the masses in the present day?

ISS PREVIOUS YEAR 2016 GS ISS PREVIOUS YEAR 2016 GS Question (d) Why were a number of European trading companies attracted to India during the 16th–17th centuries? Answer During the 16th and 17th centuries, India emerged as a major center of attraction for European trading companies such as the Portuguese, Dutch, English, and French. The primary reason was India’s immense wealth and flourishing trade in high-demand commodities like spices, cotton textiles, silk, indigo, and p

In the Gauss-Markov linear model, letŷ denote the vector of fitted values andê denote the vector of residuals. Consider the following statements: The components of ŷ are pairwise uncorrelated. The components of ê are pairwise uncorrelated.

For the distribution: f(x) = [1 / B(p, q)] × [x^(p − 1) / (1 + x)^(p + q)],where 0 < x < ∞, p > 0, q > 0, find the harmonic mean. Options: (a) p / (p + q) (b) 1 / p (c) (p − 1) / q (d) (p + 1) / (q − 1)