# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 62 - 66 of 165

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## Question number: 62

Appeared in Year: 2011

### Describe in Detail

A fair die is thrown until a 6 appears. Specify the sample space. What is the probability that it must be thrown at least 3 times?

### Explanation

A fair die content the value {1,2, 3,4, 5,6}

So, the probability of getting 6 is p = 1/6, then probability of getting other than 6 is q = 5/6

If we throw a die, the six is appear. Then the probability is p and the experiment end. However, if the six is not appear, the dice is throwing again and this time the six appear. Then the probability i

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## Question number: 63

» Probability » Conditional Probability

Appeared in Year: 2011

### Describe in Detail

Consider the following bivariate p. m. f. of (X, Y):

p (0,10) = p (0,20) = 2/18;

p (l, 10) = p (l, 30) = 3/18;

p (1,20) = p (2,30) = 4/18;

Obtain the conditional mass functions p (y lx = 2), and p (y lx = 1).

### Explanation

The joint probability is given

- | x | Total | |||

- | 0 | 1 | 2 | ||

Y | 10 | 2/18 | 3/18 | 0 | 5/18 |

20 | 2/18 | 4/18 | 0 | 6/18 | |

30 | 0 | 3/18 | 4/18 | 7/18 | |

Total | 4/18 | 10/18 | 4/18 | 1 |

First find the marginal probability of x at x = 0,1, 2

p (0) =p (0,10) +p (0,20) + p (0,30)

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## Question number: 64

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2014

### Describe in Detail

The marginal distributions of X and Y are given in the following table:

X | 1 | 2 | Total | |

Y | 3 4 | ? ? | ? ? | 1/4 3/4 |

Total | 1/2 | 1/2 | 1 |

If the co-variance between X and Y is zero, find the cell probabilities and see whether X and Y are independent.

### Explanation

Given that covariance between X and Y is zero

This gives that f (xy) =f (x) f (y)

So, the joint probability density function of x = 1, y = 3 is

We know that if the covariance is zero, then the conditional distribution is equal to unknown distribution

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## Question number: 65

» Statistical Methods » Association and Contingency

Appeared in Year: 2014

### Describe in Detail

A medicine supposed to have effect in preventing TB was treated on 500 individuals and their records were compared with the records of 500 untreated individuals as follows. Study the effectiveness of medicine by calculating (i) Yule’s coefficient of association (ii) Yule’s coefficient of colligation.

- | No-TB | TB |

Treated | 252 | 248 |

Untreated | 224 | 276 |

### Explanation

The frequencies for various attributes be show in this contingency table

- | No-TB (A) | TB (a) |

Treated (B) | (AB) | (aB) |

Untreated (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), (

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## Question number: 66

» Statistical Methods » Data » Multivariate

Appeared in Year: 2011

### Describe in Detail

The following are the frequencies in the given intervals:

| (2 - 5) | (5 - 10) | (10 - 15) | (15 - 18) | (18 - 20) | |

43 | 85 | 151 | 112 | 72 | 34 |

Draw the histogram of this data. Calculate the mean of the data from the frequency table.

### Explanation

The histogram of the frequencies is given where the widths of all classes are not equal.

Class interval | mid value | Frequencies |

(0 - 2) | 1 | 43 |

(2 - 5) | 3.5 | 85 |

(5 - 10) | 7.5 | 151 |

(10 - 15) | 12.5 | 112 |

(15 - 18) | 16.5 | 72 |

(18 - 20) | 19 | 34 |

Hence, the mean of the distribution is