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

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## Question 161

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

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…

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