# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 55 - 61 of 165

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## Question number: 55

» Statistical Methods » Non-Parametric Test » Wilcoxon

Appeared in Year: 2010

### Describe in Detail

The following data represent lifetimes (hours) of batteries for two different brands:

Brand A | 40 | 30 | 40 | 45 | 55 | 30 |

Brand B: | 50 | 50 | 45 | 55 | 60 | 40 |

Test whether two brands are the same.

### Explanation

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## Question number: 56

Appeared in Year: 2012

### Describe in Detail

Let X _{1}, X _{2}, ···, X _{n} be random variables such that

Also

Find

### Explanation

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## Question number: 57

» Probability » Standard Probability Distributions » Normal

Appeared in Year: 2011

### Describe in Detail

Let X _{1}, X _{2}, …, X _{n} be independent N (0, σ ^{2}) random variables. Obtain the mean and variance of . What is its probability distribution?

### Explanation

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## Question number: 58

» Probability » Characteristic Function

Appeared in Year: 2013

### Describe in Detail

Find the density function of X whose characteristic function Φ (t) is given by:

### Explanation

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## Question number: 59

» Statistical Methods » Tests of Significance » Chi-Square

Appeared in Year: 2010

### Describe in Detail

For 2X2 table

A | b |

C | d |

prove that Chi-square test of independence gives

### Explanation

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## Question number: 60

» Probability » Standard Probability Distributions » Uniform

Appeared in Year: 2010

### Describe in Detail

Let X be a random variable with a continuous distribution function F. Show that F (X) has the uniform distribution on (0, 1).

### Explanation

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## Question number: 61

» Probability » Standard Probability Distributions » Cauchy

Appeared in Year: 2012

### Describe in Detail

For the Cauchy distribution given by

where k is a constant to be suitably chosen, derive the expression for the distribution function. Hence obtain a measure of central tendency and a measure of dispersion. What are the points of inflexion of the distribution?

### Explanation

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