# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 78 - 83 of 165

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## Question number: 78

» Statistical Methods » Correlation Coefficient » Partial Correlation

Appeared in Year: 2014

### Describe in Detail

Given the following correlation matrix of order 3 x 3

Calculate (i) r _{12.3} (ii) r _{1.23}

### Explanation

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## Question number: 79

» Probability » Distribution Function » Standard Probability Distributions

Appeared in Year: 2013

### Describe in Detail

Find the distribution of the ratio of two iid random variables with density function:

### Explanation

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## Question number: 80

» Probability » Standard Probability Distributions » Normal

Appeared in Year: 2012

### Describe in Detail

12·3 % of the candidates in a public examination score at least 70%, while another 6·3 % score at most 30%. Assuming the underlying distribution to be normal, estimate the percentage of candidates scoring 80 % or more.

### Explanation

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## Question number: 81

» Probability » Probability of M Events Out of N

Appeared in Year: 2013

### 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

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## Question number: 82

» Probability » Probability of M Events Out of N

Appeared in Year: 2014

### Describe in Detail

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

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

### Explanation

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## Question number: 83

» Statistical Methods » Tests of Significance » F-Test

Appeared in Year: 2012

### 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

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