ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 128 - 134 of 165

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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

The marginal distribution of X is

The conditional distribution of X given Y = y

The conditional mean is

The conditional variance is

… (128 more words) …

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

… (310 more words) …

Question number: 130

» Probability » Standard Probability Distributions » Poisson

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 −1)! for r integer.

… (108 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

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

Then find the sign of difference between d i and d 0.

-+ –++

… (143 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

which is always true because this

… (134 more words) …

Question number: 133

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2010

Essay Question▾

Describe in Detail

How large a sample must be taken in order that the probability will be at least 0·95 that X n will be within 0·5 of µ (µ is unknown and σ = l).

Explanation

Here, you would know the standard deviation of a population but not know the mean of that population. So, you want to estimate the mean μ to within a given margin of error in a given confidence interval. The required sample size is

Margin of error E = 0.5,

1-α=0.95 →α=0.05

σ=1 and z α/2 =1.96

… (41 more words) …

Question number: 134

» Statistical Methods » Measures of Location

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Find the weighted arithmetic mean of the first ‘n’ natural numbers, the weights being the corresponding numbers.

Explanation

If x 1, x 2, …, x n are the values having weights w 1, w 2, …, w n respectively, the weight mean is

Here X is first ‘n’ natural numbers that is 1,2, 3, …, n

… (108 more words) …

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