# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 63 - 66 of 164

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## Question 63

Appeared in Year: *2011*

### Describe in Detail

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

p (0,10) = p (0,20) = ;

p (1,10) = p (1,30) = ;

p (1,20) = p (2,30) = ;

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

### Explanation

The joint probability is given

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

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

p (1) = p (1,10) + p (1,20) + p (1,30) =

p (2) = p (2,10) + p (2,20) + p (2,30) =

The conditional distribution of the random variable X given Y = y is

Y | 10 | 20 | 30 |

P (y|x = 2) | 0 | 0 | 1 |

Y | 10 | 20 | 30 |

P (y|x = 1) |

… (8 more words) …

## Question 64

Appeared in Year: *2014*

### Describe in Detail

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

X | 1 | 2 | Total | |

Y | 3 4 | ? ? | ? ? | |

Total | 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

Similarly, the other will obtained.

For X and Y are independent, the joint distribution is equal to the…

… (32 more words) …

## Question 65

Appeared in Year: *2014*

### Describe in Detail

Essay▾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) , (Ab) and (ab) represent the frequencies, then Yu…

… (45 more words) …

## Question 66

Appeared in Year: *2011*

### Describe in Detail

Essay▾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