ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 162 - 165 of 165

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Question number: 162

» Probability » Distribution Function » Standard Probability Distributions

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Appeared in Year: 2011

Essay Question▾

Describe in Detail

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

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Question number: 163

» Numerical Analysis » Interpolation Formulae » Gauss

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Appeared in Year: 2009

Essay Question▾

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Find the value of

by taking 5 subintervals and using the Trapezoidal rule.

Explanation

Let

First divided the interval into 5 subintervals

x

0

1/4

1/2

3/4

1

y

1

16/17

4/5

16/25

½

Here a = 0, b = 1, n = 4, h= (b-a) /n = 1/4

the Trapezoidal rule is

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Question number: 164

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

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Appeared in Year: 2015

Essay Question▾

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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

Marks

30 - 40

40 - 50

50 - 60

60 - 70

70 - 80

Number of students

31

42

51

35

31

Explanation

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

Marks less than

Number of student

Difference

∆y 0

2 y 0

3 y 0

4 y 0

x 0 =40

y 0 = 31

42

9

-25

37

50

y 1 =73

51

-16

60

y 2 =124

35

70

y 3 =159

12

80

y 4 =190

31

-4

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Question number: 165

» Statistical Methods » Association and Contingency

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Appeared in Year: 2015

Essay Question▾

Describe in Detail

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

Disease on-set

Yes

No

Medicine used

A

19

587

B

193

2741

Explanation

The frequencies for various attributes be show in this contingency table

Medicine used

Yes (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),

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