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:

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​:

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:

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.

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A certain task can be accomplished in a factory by four different workers on five different types of machines. A sample study in context of a two-way design without repeated value is being made with two fold objectives of examining whether the four workers differ with respect to mean productivity and whether it is same for five machines. The researcher involved in this study reports gathered data as under : Sum of squares for variance between machines = 35.2 Sum of squares