# 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&#8230;

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## Question 150

Edit

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&#8230;

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## Question 151

Appeared in Year: 2015

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Essay▾

For random variables X, Y, show that

We know that

## Question 152

Appeared in Year: 2010

### Describe in Detail

Essay▾

Evaluate loge 7 by Simpson՚s - rd rule.

### Explanation

We get loge 7, when

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

Where

Here,

Using Simpson՚s rule is

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## Question 153

Appeared in Year: 2015

### Describe in Detail

Essay▾

Let X1 , X2 , … , Xn be independent Poisson variates with E (Xi) = µi . Find the conditional distribution of

### Explanation

For finding the conditional distribution, first find the distribution of sum of X1 , X2 , … , Xn .

Assume that y-k = n

Similarly, for last two terms,

Given X1 , X2 , … , Xn being independent and Poisson distributed with parameters µi , i = 1,2, … , n

Then,

The conditional distribution of is

In the question that X1 , X2 , … , Xn be independent Poisson va&#8230;

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## 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 Xi is random variable of student were given different teaching methods in set I with mean and variance σ1 2 and Yj is random variable of student were given different teaching methods in set II with mean and variance σ2 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&#8230;

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## 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 Xi is random variable of nine student were tested for after training with mean and variance σ1 2 and Yj is random variable of nine student were tested for before training with mean and variance σ2 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 H0 if the&#8230;

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