# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 107 - 112 of 165

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## Question number: 107

» Probability » Tchebycheffs Inequality

Appeared in Year: 2009

### Describe in Detail

Let X ~ BIN (100,0·2). Compute P [10 ≤ X ≤ 30].

### Explanation

X ~ BIN (100,0·2), where n = 100, p = 0.2, q = 0.8

E (X) =np = 20, Var (X) =npq = 16, σ=4

Let X be a random variable with meanE (X) = µ and variance Var (X) = σ ^{2}. Then any k > 0, the Chebyshev’s inequality is

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## Question number: 108

» Numerical Analysis » Interpolation Formulae » Lagrange

Appeared in Year: 2010

### Describe in Detail

The following values of the function f (x) for values of x are given:

f (l) = 4, f (2) = 5, f (7) = 5, f (8) = 4.

Find the value of f (6) and also the value of x for which f (x) is maximum or minimum.

### Explanation

This is written in the table in this function y = f (x)

x | 1 | 2 | 7 | 8 |

y | 4 | 5 | 5 | 4 |

For find x = 6, we use Lagrange’s interpolation polynomial because the x values is not equal interval. There are four values of x which gives the y values. The Lagrange’s interpolation polynomial formula is

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## Question number: 109

» Statistical Methods » Non-Parametric Test » Mann-Whitney

Appeared in Year: 2015

### Describe in Detail

Consider the two samples as follows:

Sample I = 6,7, 8,10,12,14,16,23

Sample II: 9,11,13,15,17,18,19,20,24

Test whether the examples have come from the same population by Wilcoxon-Mann-Whitney test at 10 % level of significance. [You can use normal approximation]

### Explanation

Let the sample I consider the population X and sample II consider the population Y. The hypothesis whether two sample comes from same identical population. We test the following null and alternative hypothesis is

In Wilcoxon-Mann-Whitney test, first consider the combined ordered sequence of the sample values is

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## Question number: 110

» Statistical Methods » Regression » Linear

Appeared in Year: 2015

### Describe in Detail

For 20 pairs of heights of father (X) and son (Y) measured in cm, the following data are obtained:

Test whether the cut on the X-axis can be assumed to be zero, at 5 % level of significance.

### Explanation

In the regression model, the cut on the X-axis can be assumed to be zero means the intercept zero. The test of the hypothesis is

Can be tested by the statistic is

where is the standard error of an estimator b _{0}.

where

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## Question number: 111

» Probability » Definitions and Axiomatic Approach

Appeared in Year: 2013

### Describe in Detail

Let X have the density function,

(i) Find the constant c.

(ii) Find the distribution function.

(iii) Compute P [X > -1/2].

### Explanation

(I) To find the value of c using this density function, the integral of density is equal to one by probability definition. The range of X is|X| < 1

when X is positive, | X|=X < 1 and X is negative, | X|=-X < 1 that is X > -1

(ii) The distribution functio

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## Question number: 112

» Probability » Standard Probability Distributions » Geometric

Appeared in Year: 2012

### Describe in Detail

Write down the probability mass function of geometric distribution. State and prove its ‘lack of memory property’. Find also the mean and the variance of the distribution.

### Explanation

If there are number of trails such that the probability of success is p. So, the probability that there are x failures before the first success is

This is the probability mass function of geometric distribution

__Statement: __

Among the all discrete distributions, the geometric distribution has the lack of memory property.

__Pro__

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