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

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Question number: 125

» Probability » Standard Probability Distributions » Normal

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

f(x)=12πσe12(xμσ)2;<x<;<μ<

Let Z=X… (166 more words) …

Question number: 126

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2010

Essay Question▾

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

f(x,y)={x+y;0<x<1,0<y<10;otherwise

Obtain correlation coefficient between X and Y

Explanation

First find the marginal distribution of X

g(x)=01f(x,y)dy

=01(x+y)dy

=[xy+y22]01

=x+12… (374 more words) …

Question number: 127

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

Appeared in Year: 2013

Essay Question▾

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Solve the equation:

dydx=1y,y=0whenx=0

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

Explanation

The given differential equation is

dydx=1y=f(x,y)

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

Using Euler, s method,

yn+1=yn+hf(xn,y… (165 more words) …

Question number: 128

» Probability » Conditional Probability

Appeared in Year: 2011

Essay Question▾

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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

f(x,y)=1;0<y<x<1

The marginal distribution of X is

f(x)=011dy=1

The conditional distribution of X given… (101 more words) …

Question number: 129

» Numerical Analysis » Interpolation Formulae » Lagrange

Appeared in Year: 2012

Essay Question▾

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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

x=(yy1)(yy2)(yy3)(y0y1)(y0y2)(y0… (210 more words) …

Question number: 130

» Probability » Standard Probability Distributions » Poisson

Appeared in Year: 2015

Essay Question▾

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Prove that for r = 1, 2, …, n

1Γrμtr1etdt=x=0r1eμμxx!

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.

P(Xr1)=x=0r1eμμxx!

P(X… (271 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

H0:M1=M2VsH1:M1M2

Fir this first find the difference of median

d0=M1… (210 more words) …

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