# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 69 - 74 of 165

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## Question number: 69

» Numerical Analysis » Inverse Interpolation

Appeared in Year: 2014

### Describe in Detail

Given the following values of the function y = f (x); evaluate f (4) and also find x for which f (x) = 25.

f (1) = 10, f (2) = 15, f (3) = 42.

### Explanation

Given that y = f (x), So

x 1 2 3 4

y 10 15 42?

To find the missing value, we use binomial expansion method. Here 3 values are known, we would take third order finite difference zero. Thus,

Second question is that if we

## Question number: 70

» Probability » Distribution Function » Standard Probability Distributions

Appeared in Year: 2010

### Describe in Detail

Let (X, Y) be jointly distributed with p. d. f.

Find marginal probability density function of X and Y.

### Explanation

The marginal probability density function of X is

The range is 0 < x < 1

The marginal probability density function of Y is

The range is 0 < y < 1

## Question number: 71

» Numerical Analysis » Interpolation Formulae » Lagrange

Appeared in Year: 2010

### Describe in Detail

The observed-values of a function are respectively 168, 120, 72 and 63 at the four positions 3, 7, 9 and 10 of the independent variable. What is the best estimate you can give for the value of the function at the position 6 of the independent variable?

### Explanation

Using Lagrange’s formula

Given that a = 3, b = 7, c = 9, d = 10 and f (a) =168, f (b) =120, f (c) =72, f (d) =63

Find x = 6, the values of f (x) =?

## Question number: 72

» Statistical Methods » Non-Parametric Test » Run

Appeared in Year: 2012

### Describe in Detail

In a ticket counter, at some point of time the sequence of males (M) and females (F) was found as

MMFMFFFMFMMFFFFMFMMMM

Use runs test to examine if the sequence is random (5 % critical value of the number r of runs with n _{1 } = 11, n _{2 } = 10 is 6).

### Explanation

Suppose a sample size n contains n _{1} symbols of one type and n _{2} symbols of the other type. The null hypothesis is the symbols occur in random order. The alternative is the symbols occur in a set pattern. The lower and upper critical value is obtained from tables.

## Question number: 73

» Statistical Methods » Measures of Location

Appeared in Year: 2015

### Describe in Detail

Let X have the probability density function

Find the mean, geometric mean and harmonic mean.

### Explanation

Then mean is

The geometric mean is

The geometric mean is

The harmonic mean is

## Question number: 74

» Probability » Tchebycheffs Inequality

Appeared in Year: 2011

### Describe in Detail

Let X be a positive valued random variable. Prove that

Hence deduce the Chebychev’s inequality.

### Explanation

The expectation of X is define as

For any x ≥ r

This implies that

Hence, any function of X, assume g (x) the Chebychev’s inequality is