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
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
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
» Numerical Analysis » Numerical Integration
Appeared in Year: 2013
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
» Probability » Standard Probability Distributions » Cauchy
Appeared in Year: 2011
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
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
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) …