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

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Question number: 47

» Statistical Methods » Correlation Ratio

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

Equation

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,

Equation

Prove it

Explanation

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

Equation

Therefore Equation ………… (1)

The equation is

Equation

Equation

Equation

Equation

Using equation (1)

Equation

Equation

Equation

Since the equation is true. Therefore,

Equation

Question number: 49

» Numerical Analysis » Numerical Integration

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Evaluate the following by taking seven ordinates of the integrand:

Equation

Explanation

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

Equation

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) = Equation

Equation

Equation

Equation<span class="more">… (10 more words) …</span>

Question number: 50

» Probability » Standard Probability Distributions » Cauchy

Appeared in Year: 2011

Essay Question▾

Describe in Detail

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

Equation

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

Equation

Equation

Equation

Equation

Equation

Equation

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

Equation

Explanation

The Euler-Maclaurin formula is

Equation

where

Equation

Given the equation

Equation

Equation

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

Equation

Equation

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

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