ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 125 - 131 of 165

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Question number: 125

» Probability » Standard Probability Distributions » Normal

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Appeared in Year: 2009

Essay Question▾

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Suppose that the random variable X has a normal distribution with mean µ and variance σ 2. Let φ be the distribution function of a standard normal variate. Find the density of φ (X-µ/σ). Also find E [φ (X-µ/σ) ].

Explanation

X has a normal distribution with mean µ and variance σ 2

Let

… (131 more words) …

Question number: 126

» Statistical Methods » Correlation Coefficient » Multiple Correlation

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Appeared in Year: 2010

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Let (X, Y) be jointly distributed with density function

Obtain correlation coefficient between X and Y

Explanation

First find the marginal distribution of X

find the marginal distribution of Y

… (106 more words) …

Question number: 127

» Numerical Analysis » Summation Formula » Euler-Maclaurin's

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Appeared in Year: 2013

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Solve the equation:

Use Euler algorithm and tabulate the solution at x = 0.1,0.2,0.3.

Explanation

The given differential equation is

with initial condition x 0 = 0, y 0 = 0

Using Euler, s method,

where

We obtain y at x = 0.1

… (78 more words) …

Question number: 128

» Probability » Conditional Probability

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Appeared in Year: 2011

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Let (X, Y) have the uniform distribution over the range 0 < y· < x < 1. Obtain the conditional mean and variance of X given Y = y.

Explanation

The joint probability density function of (X, Y) is

The marginal distribution of X is

The conditional distribution of X given Y = y

The conditional mean is

… (82 more words) …

Question number: 129

» Numerical Analysis » Interpolation Formulae » Lagrange

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Appeared in Year: 2012

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Solve the equation f (x) = 0 by using a suitable interpolation formula on the following values:

x

3

4

5

6

f (x)

-2.8

-1.2

-0.3

1.8

Explanation

To solve the equation f (x) = 0, using Lagrange’s inverse interpolation method

… (170 more words) …

Question number: 130

» Probability » Standard Probability Distributions » Poisson

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Appeared in Year: 2015

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Prove that for r = 1,2, …, n

Explanation

We known that the L. H. S. is an incomplete gamma function and R. H. S. is a cumulative density function of Poisson distribution.

The incomplete gamma function is

… (96 more words) …

Question number: 131

» Statistical Methods » Non-Parametric Test » Sign

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Appeared in Year: 2011

Essay Question▾

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Let the temperature before and after administration of aspirin be

Patient

Before

After

1

100·0

98·1

2

102·1

97·2

3

100·6

98·6

4

100·1

99·1

5

101·5

97·6

6

102

98·6

7

99·9

98·2

8

102·7

98·1

9

100.40

98·2

10

100·8

97.1

Test by the sign test; whether aspirin is effective in reducing temperature. What is the p-value of the calculated statistic?

Explanation

Let M 1 and M 2 is the median temperature of the patients. The hypothesis for test is

Fir this first find the difference of median

Also find the difference of temperature of before and after

d i 2.1 4.9

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