ISS Statistics Paper I (Old Subjective Pattern): Questions 74 - 80 of 165

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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

P[Xr]E(X)r,r>0

Hence deduce the Chebychev’s inequality.

Explanation

The expectation of X is define as

E(X)=xf(x)dx

For any x ≥ r

{xr}xf(x)dx

r{xr}… (63 more words) …

Question number: 75

» Probability » Distribution Function » Standard Probability Distributions

Appeared in Year: 2015

Essay Question▾

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Let Y 1 denote the first order statistic in a random sample of size n from a distribution that has the pdf

f(x)={e(xθ),θ<x<0,otherwise

Obtain the distribution of Z n =n (Y 1 -θ).

Explanation

To find the distribution of order statistic, the pdf is

fx(j)(x)=n!(j1)!(nj)!f(x)[F(x)]j1[1F… (290 more words) …

Question number: 76

» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)

Appeared in Year: 2010

Essay Question▾

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If f (x) =1/x 2, find the divided differences f (a, b) and f (a, b, c).

Explanation

we can write the Newton’s divided difference formulas as

f(a,b)=f(b)f(a)ba

=1b21a2ba

=a2b2a2b2(… (205 more words) …

Question number: 77

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2015

Essay Question▾

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If X follows binomial b (n 1, p 1) distribution and Y follows binomial b (n 2, p 2), provide an appropriate test at level α for H 0: p 1 =p 2 against H 1: p 1 > p 2.

Explanation

The hypothesis is equivalent to testing the null hypothesis that p 1 −p 2 = 0 against the alternative is p 1 -p 2 > 0. The statistic on which we base our decision is the random variable P^1P^2. Suppose the samples of… (142 more words) …

Question number: 78

» Statistical Methods » Correlation Coefficient » Partial Correlation

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Given the following correlation matrix of order 3 x 3

R=[10.57080.673510.44871]

Calculate (i) r 12.3 (ii) r 1.23

Explanation

In general, the correlation matrix is in these notations

R=[1r12r13r211r23r31r321]

(i)

r12.3=r12r13r23(1r132)(1r… (64 more words) …

Question number: 79

» Probability » Distribution Function » Standard Probability Distributions

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Find the distribution of the ratio of two iid random variables with density function:

f(x)=ex,0<x<0,elsewhere

Explanation

Let consider x and y are two iid random variable with density function is same. Then find the distribution of their ratio that is x/y. The joint pdf of x and y is

f(x,y)=e(x+y)

To find this… (190 more words) …

Question number: 80

» Probability » Standard Probability Distributions » Normal

Appeared in Year: 2012

Essay Question▾

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12.3 % of the candidates in a public examination score at least 70%, while another 6.3 % score at most 30%. Assuming the underlying distribution to be normal, estimate the percentage of candidates scoring 80 % or more.

Explanation

Let total marks obtain is 100. Assuming the underlying distribution to be normal, the mean µ and variance σ 2. It is given that

P(X70)=P(z70μσ2)=0.123

The value of z corresponding to… (173 more words) …

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