ISS PREVIOUS YEAR 2016 PAPER-1 SET-A To compare the lifetimes of bulbs produced by two companies A and B, one bulb from each company was selected at random and their lifetimes were observed. Assume that the lifetimes follow exponential distributions with: Mean(A) = 1000 daysMean(B) = 800 days What is the probability that the bulb from company B fails before the bulb from company A? Options: (a) 4/9 (b) 5/9 (c) 25/81 (d) 25/41

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.

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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​ ?

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

It is often stressful, overwhelming, and exhausting to prepare for examinations. One of the biggest challenges that students face is to maintain their level of motivation during their examination preparation journey. However, with the right mindset, it is easy to maintain motivation and do your best.

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)

One of the most common questions students ask while preparing for government exams is: “How many hours should I study every day?” Many students feel that they need to study 12–14 hours daily to succeed. But the truth is a little different.

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.

Government exams in India are highly competitive. Every year, lakhs of students apply for various exams such as banking, SSC, railways, teaching services, and statistical services. While many students work hard, only a small percentage achieve success.

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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?