# ISS Statistics Paper I (Old Subjective Pattern): Questions 126 - 132 of 165

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## Question number: 126

» Statistical Methods » Correlation Coefficient » Multiple Correlation

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

The mean of X and Y is

The second moment of X and Y is

The variance of X and Y… (24 more words) …

## Question number: 127

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

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

Again obtain y at x = 0.2

Similarly y at x = 0.3… (18 more words) …

## Question number: 128

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

The conditional variance is

## Question number: 129

» Numerical Analysis » Interpolation Formulae » Lagrange

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

## Question number: 130

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

Then

provided that r is an integer. Thus recall that Γ (r) = (r… (20 more words) …

## Question number: 131

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 2.0 1.0 3.9 3.4 1.7 4.6 2.4 3.7… (131 more words) …

## Question number: 132

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2010

Essay Question▾

### Describe in Detail

Show that for discrete distribution β 2 > 1

### Explanation

We have to prove that

By definition of Kurtosis

Let x 1, x 2, …, x n are n observations in a set have frequency f 1, f 2, …, f n and the mean of observation is , then

Assume

f Page