# ISS Statistics Paper I (Old Subjective Pattern): Questions 47 - 52 of 165

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## Question number: 47

Appeared in Year: 2012

Essay Question▾

### Describe in Detail

Scores in a UPSC examination in Statistics Paper-I and Paper-II awarded to10 candidates were as under:

 Candidate A B C D E F G H I J Score in Paper- I 91 65 80 120 80 140 105 80 42 72 Score in Paper-II 86 38 75 135 85 135 94 101 45 65

Calculate Spearman’s rank correlation coefficient between the scores in the two papers.

### Explanation

The method of calculating the association between the ranks is known as Spearman’s rank correlation. The candidates are rank by the UPSC examination taken for two papers which is independent. The Spearman’s rank correlation is

where n is the number of candidates and d i is the difference between… (94 more words) …

## Question number: 48

» Probability » Standard Probability Distributions » Geometric

Appeared in Year: 2010

Essay Question▾

### Describe in Detail

Let X have a geometric distribution, then for an two non-negative integers m and n,

Prove it

### Explanation

This proof is a lack of memory property. We known that

Therefore ………… (1)

The equation is

Using equation (1)

Since the equation is true. Therefore,

## Question number: 49

Appeared in Year: 2013

Essay Question▾

### Describe in Detail

Evaluate the following by taking seven ordinates of the integrand:

### Explanation

The seven ordinates of the integrand using Simpson’s rule is

Where h = 1/6 (b-a) and y k =f (a + kh) for k = 0, 1, 2, 3, 4, 5, 6

Here, b = 1, a = 0, h = 1/6, f (x) =

## Question number: 50

Appeared in Year: 2011

Essay Question▾

### Describe in Detail

Obtain the median and the quartiles of the Cauchy distribution with p. d. f.

### Explanation

For find the median and quartile of the Cauchy distribution, q is any quartile. Then, for which value of q, the x value is

For first quartile q = 1/4, then x=-1

For median q = 1/2, then x = 0

For third quartile… (7 more words) …

## Question number: 51

» Numerical Analysis » Summation Formula » Euler-Maclaurin's

Appeared in Year: 2015

Essay Question▾

### Describe in Detail

By using Euler-Maclaurin formula, find the sum

### Explanation

The Euler-Maclaurin formula is

where

Given the equation

## Question number: 52

» Statistical Methods » Order Statistics » Maximum

Appeared in Year: 2014

Essay Question▾

### Describe in Detail

Let X 1, X 2, …, X n be n independently identically distributed random variables following an exponential distribution with mean parameter θ. Obtain the distributions of (i) Maximum (X 1, X 2, …, X n); (ii) Minimum (X 1, X 2, …, X n) and (iii) Median for n = 2m + 1, (m > 0)

### Explanation

Let X 1, X 2, …, X n, be n independently identically distributed random variables following an exponential distribution with mean parameter θ. The probability density and distribution function is

Let X (1) , X (2) , …, X (n) denote the order statistic of… (129 more words) …

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