ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 69 - 74 of 165

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Question number: 69

» Numerical Analysis » Inverse Interpolation

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Appeared in Year: 2014

Essay Question▾

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Given the following values of the function y = f (x); evaluate f (4) and also find x for which f (x) = 25.

f (1) = 10, f (2) = 15, f (3) = 42.

Explanation

Given that y = f (x), So

x 1 2 3 4

y 10 15 42?

To find the missing value, we use binomial expansion method. Here 3 values are known, we would take third order finite difference zero. Thus,

… (72 more words) …

Question number: 70

» Probability » Distribution Function » Standard Probability Distributions

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Appeared in Year: 2010

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Let (X, Y) be jointly distributed with p. d. f.

Find marginal probability density function of X and Y.

Explanation

The marginal probability density function of X is

The range is 0 < x < 1

The marginal probability density function of Y is

… (61 more words) …

Question number: 71

» Numerical Analysis » Interpolation Formulae » Lagrange

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Appeared in Year: 2010

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The observed-values of a function are respectively 168,120,72 and 63 at the four positions 3,7, 9 and 10 of the independent variable. What is the best estimate you can give for the value of the function at the position 6 of the independent variable?

Explanation

Using Lagrange’s formula

… (167 more words) …

Question number: 72

» Statistical Methods » Non-Parametric Test » Run

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Appeared in Year: 2012

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In a ticket counter, at some point of time the sequence of males (M) and females (F) was found as

MMFMFFFMFMMFFFFMFMMMM

Use runs test to examine if the sequence is random (5 % critical value of the number r of runs with n 1 = 11, n 2 = 10 is 6).

Explanation

Suppose a sample size n contains n 1 symbols of one type and n 2 symbols of the other type. The null hypothesis is the symbols occur in random order. The alternative is the symbols occur in a set pattern. The lower and upper critical value is obtained from tables. If the observed number of runs in a sample lies in between these critical values, t

… (61 more words) …

Question number: 73

» Statistical Methods » Measures of Location

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Appeared in Year: 2015

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Let X have the probability density function

Find the mean, geometric mean and harmonic mean.

Explanation

Then mean is

The geometric mean is

… (102 more words) …

Question number: 74

» Probability » Tchebycheffs Inequality

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Appeared in Year: 2011

Essay Question▾

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Let X be a positive valued random variable. Prove that

Hence deduce the Chebychev’s inequality.

Explanation

The expectation of X is define as

For any x≥r

This implies that

Hence, any function of

… (75 more words) …