ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 82 - 86 of 165

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Question number: 82

» Probability » Probability of M Events Out of N

Appeared in Year: 2014

Essay Question▾

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A positive integer X is selected at random from the first 50 natural numbers.

Calculate P (X + 96/X > 50).

Explanation

Total number of possible outcomes = number of ways in which the one random number can be chosen out of 50

Equation

Let Y be the event whose satisfied the relation, X + 96/X > 50

For which X we choose is

Equation

Equation

Equation

Equation

So, X takes values… (38 more words) …

Question number: 83

» Statistical Methods » Tests of Significance » F-Test

Appeared in Year: 2012

Essay Question▾

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Indicate how you would test the hypothesis that the means of k independent normal populations are identical, clearly mentioning the null and the alternative hypotheses, the assumptions made, the test statistic used, and the critical region.

Explanation

Let there are k independent normal population Equation with different sample size n 1, n 2, …, n k. The test of null hypothesis is that the means of k normal population is same and the alternative hypothesis is any two mean are not same.

Equation Vs… (75 more words) …

Question number: 84

» Statistical Methods » Regression » Linear

Appeared in Year: 2011

Essay Question▾

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From a bivariate data set of 4995 observations, the following quantities have been calculated:

Equation

Obtain the estimated linear regression of X on Y.

Explanation

Let the linear equation is

Equation

To solve this equation by least square method. In this approach, the residual sum of squares is minimized by partially differentiating with respect to Equation and Equation.

Equation

To differential this, we get the estimate of Equation and Equation

Equation

Equation

The given… (24 more words) …

Question number: 85

» Probability » Elements of Measure Theory

Appeared in Year: 2014

Essay Question▾

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Suppose that all the four outcomes 0 1, 0 2, 0 3 and 0 4 of an experiment are equally likely. Define A = (0 1, 0 4), B = (0 2, 0 4) and C = (0 3, 0 4). What can you say about the pairwise independence and mutually independence of the events A, B and C?

Explanation

Given that there are four outcomes. Define A = (O 1, O 4), B = (O 2, O 4), C = (O 3, O 4)

Their intersection is Equation and Union is AUBUC = (O 1, O 2, O 3, O… (114 more words) …

Question number: 86

» Statistical Methods » Tests of Significance » F-Test

Appeared in Year: 2013

Essay Question▾

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Obtain 100 (1 -α) % confidence interval for the ratio of population variances by using two independent random samples from N (µ 1, σ 12) and N (µ 2, σ 22) under the assumption that the population means are (i) known and (ii) unknown.

Explanation

Let X 1, X 2, …, X n and Y 1, Y 2, …Y m are the samples taken from independent N (µ 1, σ 12) and N (µ 2, σ 22).

In this question the hypothesis for testing is… (128 more words) …

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