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

Equation

Obtain correlation coefficient between X and Y

Explanation

First find the marginal distribution of X

Equation

Equation

Equation

Equation

find the marginal distribution of Y

Equation

Equation

Equation

Equation

The mean of X and Y is

Equation

Equation

Equation

Equation

The second moment of X and Y is

Equation

Equation

Equation

Equation

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:

Equation

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

Explanation

The given differential equation is

Equation

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

Using Euler, s method,

Equation

where

Equation

We obtain y at x = 0.1

Equation

Equation

Equation

Again obtain y at x = 0.2

Equation

Equation

Equation

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

Question number: 128

» Probability » Conditional Probability

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

Equation

The marginal distribution of X is

Equation

The conditional distribution of X given Y = y

Equation

The conditional mean is

Equation

Equation

The conditional variance is

Equation

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

Equation

Equation

Equation

Equation

Equation

Question number: 130

» Probability » Standard Probability Distributions » Poisson

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Prove that for r = 1, 2, …, n

Equation

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.

Equation

Equation

The incomplete gamma function is

Equation

Then

Equation

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

Question number: 131

» Statistical Methods » Non-Parametric Test » Sign

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

Equation

Fir this first find the difference of median

Equation

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

Equation

By definition of Kurtosis

Equation

Equation

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 Equation, then

Equation

Assume Equation<span class="more">… (17 more words) …</span>

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