ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 116 - 121 of 164

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Question 116

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Appeared in Year: 2013

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Essay▾

Describe the run test for randomness. For the sequence of outcomes of 14 tosses of a coin,

HTTHHHTHTTHHTH, .

test whether the outcomes are in random order. (Given the lower and upper critical values RL = 3,

Ru = 12 at 0.05 significance level.)

Explanation

Suppose a sample size n contains n1 symbols of one type and n2 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. If the observed number of runs in a sample lies in between these critical values, the n…

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Question 117

Newton (Dividend Difference)
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Appeared in Year: 2011

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Essay▾

Use Simpson՚s rule with five ordinates to compute an approximation to π with the help of the integration of the function (1 + x 2) -1 from 0 to 1.

Explanation

T he rule of the integrand using Simpson՚s rule for five ordinates is

where , n = 5

We divide the range 0 to 1 in five equal part i.e..

Use Simpson՚s rule

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Question 118

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Appeared in Year: 2015

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Essay▾

Let X follow log-normal with parameters µ and σ 2 . Find the distribution of Y = aX b , a > 0, - ∞ < b < ∞

Explanation

If X follow log-normal with parameters µ and σ 2 , then Z = logX follow normal distribution.

First find the cdf of Y

Let

The upper limit is c = , lower limit is

Putting the value of c

The distribution of Y is

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Question 119

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Appeared in Year: 2015

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Essay▾

With 3 variables X1 , X2 and X3 , it is given that r13 = 0.71, R1.23 = 0.78. Find r12.3 .

Explanation

We know that

The relationship between the partial and multiple correlations is

Question 120

Appeared in Year: 2012

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Essay▾

For a set of 10 pairs of observations (xi , yj) , i = 1 (1) 10, the following calculations are available

Examine at 5 % level of significance if the two variables arc uncorrelated in the population.

Explanation

First, we calculate the sample correlation coefficient r

for i = 1 to 10

Putting the value in the formula for n = 10

The test hypothesis is

The test statistic is the t-test

The tabulated value is t0.05,8 = 2.306

Since the calculated value is less than the tabulated value of t, we accept Ho . It means that there is no correlation between x and y variable.

Question 121

Appeared in Year: 2009

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Essay▾

Find the density, if its characteristic function is

Explanation

Rewrite the characteristic function Φ (t)

The density function of X is given by Fourier inversion theorem using the characteristic function,

The general form is

Putting the characteristic function

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