ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 75 - 80 of 165

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Question number: 75

» Probability » Distribution Function » Standard Probability Distributions

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Appeared in Year: 2015

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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

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

Explanation

To find the distribution of order statistic, the pdf is

Here denote the first order statistic that is

The cdf of x is

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Question number: 76

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

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Appeared in Year: 2010

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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

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Question number: 77

» Statistical Methods » Tests of Significance » Z-Test

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Appeared in Year: 2015

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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 . Suppose the samples of sizes n 1 and n 2 are selected from binomial populations are independent.

For large sample size, the estim

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Question number: 78

» Statistical Methods » Correlation Coefficient » Partial Correlation

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Appeared in Year: 2014

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Given the following correlation matrix of order 3 x 3

Calculate (i) r 12.3 (ii) r 1.23

Explanation

In general, the correlation matrix is in these notations

(i)

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Question number: 79

» Probability » Distribution Function » Standard Probability Distributions

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Appeared in Year: 2013

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

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

To find this we use Jacobian transformation technique, assume

X/Y = u, Y = v

X = uv and Y = v

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Question number: 80

» Probability » Standard Probability Distributions » Normal

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Appeared in Year: 2012

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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

The value of z corresponding to an area

0.500 - 0.123 = 0.377

We can write

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