# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 149 - 155 of 164

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## Question 149

Appeared in Year: *2013*

### Describe in Detail

Essay▾For the following frequency distribution on 229 values:

Class | Frequency |

0 - 10 | 12 |

10 - 20 | 30 |

20 - 30 | x |

30 - 40 | 65 |

40 - 50 | y |

50 - 60 | 25 |

60 - 70 | 18 |

the median is found to be 46. Find the values of x and y.

### Explanation

The cumulative frequency is

Class | Frequency | Cumulative frequency |

0 - 10 | 12 | 12 |

10 - 20 | 30 | 42 |

20 - 30 | x | 42 + x |

30 - 40 | 65 | 107 + x |

40 - 50 | y | 107 + x + y |

50 - 60 | 25 | 132 + x + y |

60 - 70 | 18 | 150 + x + y |

Median is 46 which lies in the class 40 - 50. So, median class is 40 - 50.

Here n = 229, l = lower limit of median class = 40

cf = cumulative frequency of the above median class = 1…

… (38 more words) …

## Question 150

Appeared in Year: *2009*

### Describe in Detail

Essay▾Explain “Memoryless property” of a distribution. Show that the exponential distribution has memoryless property.

### Explanation

The property of memory less is that these distributions of ″ time from now to the next period ″ are exactly the same. The property is most easily explained in terms of ″ waiting times.

Suppose X is a discrete random variable whose values is a non-negative. In probability theory, a distribution is said to have lack of memory if

The lack of memory prop…

… (66 more words) …

## Question 151

Appeared in Year: *2015*

### Describe in Detail

Essay▾For random variables X, Y, show that

### Explanation

We know that

## Question 152

Appeared in Year: *2010*

### Describe in Detail

Essay▾Evaluate log_{e} 7 by Simpson՚s - rd rule.

### Explanation

We get log_{e} 7, when

So, the seven ordinates of the integrand using Simpson՚s rule is

Where

Here,

Using Simpson՚s rule is

… (4 more words) …

## Question 153

Appeared in Year: *2015*

### Describe in Detail

Essay▾Let X_{1} , X_{2} , … , X_{n} be independent Poisson variates with E (X_{i}) = µ_{i} . Find the conditional distribution of

### Explanation

For finding the conditional distribution, first find the distribution of sum of X_{1} , X_{2} , … , X_{n} .

Assume that y-k = n

Similarly, for last two terms,

Given X_{1} , X_{2} , … , X_{n} being independent and Poisson distributed with parameters µ_{i} , i = 1,2, … , n

Then,

The conditional distribution of is

In the question that X_{1} , X_{2} , … , X_{n} be independent Poisson va…

… (21 more words) …

## Question 154

Appeared in Year: *2009*

### Describe in Detail

Essay▾Two set of students were given different teaching methods. Their IQ՚s are given below:

Set I | 77 | 74 | 82 | 73 | 87 | 69 | 66 | 80 |

Set II | 72 | 68 | 76 | 68 | 84 | 68 | 61 | 76 |

Test whether the two teaching methods differ significantly at 5 % level of significance. (Assume critical value of test statistic to be 1·96)

### Explanation

Let X_{i} is random variable of student were given different teaching methods in set I with mean and variance σ_{1} ^{2} and Y_{j} is random variable of student were given different teaching methods in set II with mean and variance σ_{2} ^{2} . The hypothesis is

The sample size is n = 8

then test statistic is

The critical value of test statistic to be 1.96

The test cr…

… (23 more words) …

## Question 155

Appeared in Year: *2013*

### Describe in Detail

Essay▾The memory capacities ·of nine student were tested before and after some training. The data are given below. Test whether the training was effective: (Given t-value at 8 d. f. = 2.36)

Student Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

Before Training | 10 | 15 | 9 | 3 | 7 | 12 | 16 | 17 | 4 |

After Training | 12 | 17 | 8 | 5 | 6 | 11 | 18 | 20 | 3 |

### Explanation

Let X_{i} is random variable of nine student were tested for after training with mean and variance σ_{1} ^{2} and Y_{j} is random variable of nine student were tested for before training with mean and variance σ_{2} ^{2} . The hypothesis is

The sample size is n = 9

Population variance is known and unknown, then test statistic is

The test criteria are reject H_{0} if the…

… (22 more words) …