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

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:

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:

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

X₁ and X₂ are independent Poisson random variables such that: P(X₁ = 2) = P(X₁ = 1)P(X₂ = 2) = P(X₂ = 3) Find the variance of (X₁ − 2X₂).

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