ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 42 - 47 of 165

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Question number: 42

» Probability » Tchebycheffs Inequality

Appeared in Year: 2013

Essay Question▾

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Let X be a random variable with E [X] = 4 and E [X 2] = 20. Use Chebyshev’s inequality to determine a lower bound for the probability P [0 < x < 8].

Explanation

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Question number: 43

» Probability » Probability Generating Functions

Appeared in Year: 2014

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Let P (s) be the probability generating function associated with a non-negative, integer valued random variable X. Show that

Explanation

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Question number: 44

» Probability » Bayes' Theorem

Appeared in Year: 2014

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There are three identical bags U 1, U 2 and U 3. U 1 contains 3 red and 4 black balls; U 2 contains 4 red and 5 black balls; U 3 contains 4 red and 4 black balls. One bag is chosen at random; a ball is drawn at random from the chosen bag and it is found to be red. Find the probability that the first bag is chosen.

Explanation

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Question number: 45

» Statistical Methods » Measures of Location

Appeared in Year: 2010

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Show that for any discrete distribution, standard deviation is not less than mean deviation from mean.

Explanation

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Question number: 46

» Statistical Methods » Non-Parametric Test » Mann-Whitney

Appeared in Year: 2014

Essay Question▾

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Consider two samples as follows:

Sample 1: 1, 4, 7, 9, 16, 17, 22, 24

Sample 2: 2, 6, 10, 12, 18, 20, 26, 28, 32

Test whether the examples have come from the same population by Wilcoxon-Mann-Whitney test. [Given value of Z for α = 0·05 = 1·645, where Z is N (0, 1) ]

Explanation

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Question number: 47

» Statistical Methods » Correlation Ratio

Appeared in Year: 2012

Essay Question▾

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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

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