ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 161 - 164 of 164

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Question 161

Standard Probability Distributions

Appeared in Year: 2011

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Essay▾

Show that is a probability density function for an appropriate value of a. Upto what order do the moments of this p. d. f. exist?

Explanation

To find the value of a, we known that the probability density function under the range of x is equal to one.

To find order which is exist for this p. d. f. is

Upto moments is exist is k-2 < 0 = k < 2

That is only we find the first moment for k = 1 which is mean

Question 162

Appeared in Year: 2009

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Essay▾

Find the value of

by taking 5 subintervals and using the Trapezoidal rule.

Explanation

Let

First divided the interval into 5 subintervals

Sub-Intervals
x01
y1

Here

the Trapezoidal rule is

Question 163

Newton (Dividend Difference)

Appeared in Year: 2015

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Essay▾

By making use of difference table and a suitable interpolation formula, find the number of student who obtained less than 45 marks in an examination, from the following table

Marks30 - 4040 - 5050 - 6060 - 7070 - 80
Number of students3142513531

Explanation

Applying Newton-Gregory forward formula for interpolating the number of student who obtained less than 45 marks in an examination.

The Newton՚s formula is

where

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Question 164

Appeared in Year: 2015

Describe in Detail

Essay▾

Compute Yule՚s coefficient of association (Q) and Yule՚s coefficient of colligation (Y) for the following table:

Disease on-set
YesNo
Medicine usedA19587
B1932741

Explanation

The frequencies for various attributes be show in this contingency table

Medicine usedYes (A)No (a)
A (B)(AB)(aB)
B (b)(Ab)(ab)

(i) Yule՚s coefficient of association is a relative measure of association between two attributes, for this question the attributes are No-TB and treatment. If (AB) , (aB) , (Ab) and (ab) represent the frequencies, then Yule՚s…

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