# 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

### Describe in Detail

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

### Describe in Detail

Essay▾

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 y 1

Here

the Trapezoidal rule is

## Question 163

Newton (Dividend Difference)

Appeared in Year: 2015

### Describe in Detail

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

 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.

The Newton՚s formula is

where

… (26 more words) …

## 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 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) , (aB) , (Ab) and (ab) represent the frequencies, then Yule՚s…

… (46 more words) …