ISS PREVIOUS YEAR 2016 PAPER-1 SET-A The lifetime of a bulb follows an exponential distribution with mean 100 hours. The bulb is switched on for exactly 4 hours every day and remains switched off for the remaining time. What is the probability that the bulb stops working on or before the 25th day? Options: (a) (1 − e⁻¹) / (1 − e⁻¹⁄²⁵) (b) 1 − e⁻¹⁄²⁵ (c) 1 − e⁻¹ (d) e⁻¹

ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION A company used three different methods to train its employees. The number of units of output produced by different employees trained by the three training methods are given below: Method A: 50, 45, 55, 44 Method B: 64, 48, 52, 56, 44 Method C: 46, 42, 48, 45, 57, 42 The estimate of the population variance on the basis of the variance among the sample means for the above methods is:

What are the differences between Himalayan rivers and Peninsular rivers? Discuss.

ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION SET-A

ISS PREVIOUS YEAR 2016 PAPER-1 SET-A 10 balls are placed in 10 boxes independently and uniformly at random. Initially, all boxes are empty. What is the expected number of boxes that remain empty?

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​ ?

A simple random sample of size 10 is selected with replacement from a population of size 100. What is the expected number of unique elements in the sample? Options:(a) 100 × (99/100)¹⁰(b) 100 × [1 − (99/100)¹⁰](c) 100 × (9/10)¹⁰(d) 100 × (1 − 99/100)¹⁰

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: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

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).

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?

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)

The Indian Statistical Service (ISS) exam is a highly specialized and competitive examination that demands strong conceptual clarity and consistent practice. Many aspirants often ask: “How should I study daily?” “What routine should I follow to crack ISS?”

The division of India into provinces and the evolution of a system of provincial administration by Akbar was an effective system of governance. Comment.