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)

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

ISS PREVIOUS YEAR PAPER-1 2016 SOLUTION. The following data pertain to a test involving analysis of variance: Estimate of population variance based on variance among the sample means = 18.50. Estimate of the population variance based on the variance within the samples = 12.50 The F-ratio for the sample is equal to: Options:(a) 0.68(b) 1.48(c) 6.00(d) 31.00

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).

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

If in 6 trials, X is a binomial variate which follows the relation 9 P(X = 4) = P(X = 2) then what is the probability of success? Options:(a) 1/8 (b) 1/4 (c) 3/8 (d) 3

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Discuss the role of intellectuals in giving shape to the nationalism in India during the freedom struggle.

Let y = (y1, y2, …, yn)' be the vector of these variables. Suppose y' A y is a quadratic form where A is an idempotent matrix. What will be the distribution of y' A y?

Let X have a Bernoulli distribution with mean 0.4. What is the variance of (2X − 3)? Options: (a) 0.24(b) 0.48(c) 0.60(d) 0.96

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iss previous year solution paper-2 q.no.1