# Probability (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 20 - 26 of 72

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to **165** questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.

Rs. 550.00 or

## Question number: 20

» Probability » Standard Probability Distributions » Geometric

Appeared in Year: 2010

### Describe in Detail

Let X have a geometric distribution, then for an two non-negative integers m and n,

Prove it

### Explanation

… (26 more words) …

## Question number: 21

» Probability » Standard Probability Distributions » Cauchy

Appeared in Year: 2011

### Describe in Detail

Obtain the median and the quartiles of the Cauchy distribution with p. d. f.

### Explanation

… (48 more words) …

## Question number: 22

» Probability » Characteristic Function

Appeared in Year: 2015

### Describe in Detail

Obtain the characteristic function of X whose pdf is

### Explanation

… (140 more words) …

## Question number: 23

» Probability » Expectation

Appeared in Year: 2013

### Describe in Detail

Let X be a continuous random variable and have F (x) as the distribution function. If E [X] exists, then show that:

### Explanation

… (45 more words) …

## Question number: 24

» Probability » Expectation

Appeared in Year: 2012

### Describe in Detail

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

Also

Find

### Explanation

… (23 more words) …

## Question number: 25

» 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

… (52 more words) …

## Question number: 26

» 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

… (30 more words) …