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

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to 165 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.

Rs. 550.00 or

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

rs=16idi2n(n2… (144 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,

P(X>m+n X>m)=P(Xn)

Prove it

Explanation

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

P(Xn)=1qn+1

Therefore P(Xn)=qn+1 ………… (1)

The equation is

P(X>m+nX>… (154 more words) …

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:

0111+x2dx

Explanation

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

abf(x)dxh3(y0+4y1+2y2+4y3+2y4+4y5+y6)

Where… (198 more words) …

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.

f(x)=1π(1+x2);<x<

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

P[X<x]=xf(t)dt=q

1πx1… (84 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

1512+1532++1992

Explanation

The Euler-Maclaurin formula is

k=ab1f(k)=abf(x)dx12{f(b)f(a)}+r=1mB2r2r… (229 more words) …

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

fX(x)=1θexθ;θ>0… (514 more words) …

f Page
Sign In