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

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## Question number: 125

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Appeared in Year: 2009

Essay Question▾

### Describe in Detail

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

Essay Question▾

### Describe in Detail

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

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## Question number: 127

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

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Appeared in Year: 2013

Essay Question▾

### Describe in Detail

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

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## Question number: 128

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Appeared in Year: 2011

Essay Question▾

### Describe in Detail

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

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## Question number: 129

» Numerical Analysis » Interpolation Formulae » Lagrange

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Appeared in Year: 2012

Essay Question▾

### Describe in Detail

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

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## Question number: 130

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Appeared in Year: 2015

Essay Question▾

### Describe in Detail

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

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## Question number: 131

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Appeared in Year: 2011

Essay Question▾

### Describe in Detail

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

… (155 more words) …