ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 119 - 124 of 165

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Question number: 119

» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)

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Appeared in Year: 2012

Essay Question▾

Describe in Detail

An unknown function u x has been tabulated below for some selected values of x. Use Newton’s divided difference formula on these to find an approximate value of u 3:

x

0

2

5

10

u x

3

19

73

223

Explanation

The Newton’s divided difference formula is used when the x-values not equally spaced. The Newton’s formula of divided difference for estimating u x corresponding to x is

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Question number: 120

» Statistical Methods » Correlation Coefficient » Multiple Correlation

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Appeared in Year: 2015

Essay Question▾

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With 3 variables X 1, X 2 and X 3, it is given that r 13 =0.71, R 1.23 =0.78. Find r 12.3.

Explanation

We know that

The relationship between the partial and multiple correlations is

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Question number: 121

» Statistical Methods » Correlation Coefficient » Intraclass Correlation

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Appeared in Year: 2012

Essay Question▾

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For a set of 10 pairs of observations (x i, y j), i = 1 (1) 10, the following calculations are available

Examine at 5 % level of significance if the two variables arc uncorrelated in the population.

Explanation

First, we calculate the sample correlation coefficient r

for i = 1 to 10

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Question number: 122

» Probability » Characteristic Function

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Appeared in Year: 2009

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Find the density, if its characteristic function is

Explanation

Rewrite the characteristic function Φ (t)

The density function of X is given by Fourier inversion theorem usin

… (84 more words) …

Question number: 123

» Probability » Standard Probability Distributions » Lognormal

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Appeared in Year: 2014

Essay Question▾

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If f x (x) be the probability density function of a lognormal distribution, show that

Where and upper limit is and φ (z) is the distribution function of the standard normal distribution. Hence find E (X) and V (X).

Explanation

Given that f X (x) has a lognormal distribution, the probability density function is

Then

………

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Question number: 124

» Probability » Conditional Probability

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Appeared in Year: 2009

Essay Question▾

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(i) Let X be a random variable such that P [X < 0] = 0 and E [x] exist. Show that P (X ≤2E [x] ) ≥l/2

(ii) Let E [X] = 0 and E [X 2] be finite. Show that P (X 2 < 9E [X 2] ) > 8/9

Explanation

(i) Using Markov inequality, for any random variable and constant a > 0

Here a = 2E (X)

or

(ii) Using Chebyshev inequ

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