# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 151 - 156 of 165

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## Question number: 151

» Probability » Standard Probability Distributions » Exponential

Appeared in Year: 2009

### Describe in Detail

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

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## Question number: 152

Appeared in Year: 2015

### Describe in Detail

For random variables X, Y, show that

### Explanation

We know that

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## Question number: 153

» Numerical Analysis » Interpolation Formulae » Newton-Gregory

Appeared in Year: 2010

### Describe in Detail

Evaluate log _{e} 7 by Simpson’s -1/3rd rule.

### Explanation

We get log _{e} 7, when

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

Where h = 1/6 (b-a) and y _{k} =f (a + kh) for k = 1,2, 3,4, 5,6, 7

Here, b = 7, a = 1, h = 1, f (x) =

Using Simpson’s rule is

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## Question number: 154

» Probability » Conditional Probability

Appeared in Year: 2015

### Describe in Detail

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,

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## Question number: 155

» Statistical Methods » Tests of Significance » T-Test

Appeared in Year: 2009

### Describe in Detail

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 tes

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## Question number: 156

» Statistical Methods » Tests of Significance » T-Test

Appeared in Year: 2013

### Describe in Detail

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 kno

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