ISS 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

Essay Question▾

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,

Equation

Equation

Equation

Equation

Second question is that if we… (22 more words) …

Question number: 70

» Probability » Distribution Function » Standard Probability Distributions

Appeared in Year: 2010

Essay Question▾

Describe in Detail

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

Equation

Find marginal probability density function of X and Y.

Explanation

The marginal probability density function of X is

Equation

Equation

Equation

The range is 0 < x < 1

The marginal probability density function of Y is

Equation

Equation

Equation

The range is 0 < y < 1

Question number: 71

» Numerical Analysis » Interpolation Formulae » Lagrange

Appeared in Year: 2010

Essay Question▾

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

Equation

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) =?

Equation

Equation

Equation

Equation

Equation

Question number: 72

» Statistical Methods » Non-Parametric Test » Run

Appeared in Year: 2012

Essay Question▾

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.… (93 more words) …

Question number: 73

» Statistical Methods » Measures of Location

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let X have the probability density function

Equation

Find the mean, geometric mean and harmonic mean.

Explanation

Then mean is

Equation

Equation

Equation

Equation

The geometric mean is

Equation

Equation

Equation

Equation

The geometric mean is

Equation

The harmonic mean is

Equation

Equation

Equation

Equation

Question number: 74

» Probability » Tchebycheffs Inequality

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Let X be a positive valued random variable. Prove that

Equation

Hence deduce the Chebychev’s inequality.

Explanation

The expectation of X is define as

Equation

For any x ≥ r

Equation

Equation

Equation

This implies that

Equation

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

Equation

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