# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 81 - 85 of 165

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## Question number: 81

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Appeared in Year: 2013

Essay Question▾

### Describe in Detail

A fair die is rolled twice. Let A be the event that the first throw shows a number ≤ 2, and B be the event that the second throw shows at least 5. Show that P (AUB) =5/9.

### Explanation

A fair die is rolled twice, the sample space consists of thirty six outcomes. The sample space is

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (5,5)

… (67 more words) …

## Question number: 82

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Appeared in Year: 2014

Essay Question▾

### Describe in Detail

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

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

For which X we choose is

… (62 more words) …

## Question number: 83

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Appeared in Year: 2012

Essay Question▾

### Describe in Detail

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 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.

… (108 more words) …

## Question number: 84

» Statistical Methods » Regression » Linear

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Appeared in Year: 2011

Essay Question▾

### Describe in Detail

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

Obtain the estimated linear regression of X on Y.

### Explanation

Let the linear equation is

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

To differential this, we get the es

… (51 more words) …

## Question number: 85

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Appeared in Year: 2014

Essay Question▾

### Describe in Detail

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 and Union is AUBUC = (O 1, O 2, O 3, O 4)

P (A) = P (B) = P (C) = 1/2

P (AUBUC) =

… (137 more words) …