# 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

Appeared in Year: 2011

### 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

Appeared in Year: 2009

### Describe in Detail

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)

Appeared in Year: 2015

### Describe in Detail

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 | ∆ | ∆ | ∆ | ||

x | y | 42 | 9 | -25 | 37 |

50 | y | 51 | -16 | ||

60 | y | 35 | |||

70 | y | 12 | |||

80 | y | 31 | -4 |

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## Question number: 165

» Statistical Methods » Association and Contingency

Appeared in Year: 2015

### 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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