# Probability-Probability Generating Functions [ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)]: Questions 1 - 4 of 4

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## Question number: 1

» Probability » Probability Generating Functions

Appeared in Year: 2013

### Describe in Detail

Let P (z) be the probability generating function of the random variable X whose probability distribution is Pr [X = n] = p _{n}, n = 0, I, 2, …… Find the generating function of (i) Pr [X > n],

(ii) Pr [X < n] and (iii) Pr [X = 2n].

### Explanation

Let P (z) be the probability generating function of the random variable X whose probability distribution is Pr [X = n] = p _{n}. Then

(i) The generating function of Pr [X > n] is denoted by P (z _{> n})

The generating function is

… (397 more words) …

## Question number: 2

» Probability » Probability Generating Functions

Appeared in Year: 2009

### Describe in Detail

Given the distribution function

find its probability density function.

### Explanation

The distribution function written in this form

The density function is

where

## Question number: 3

» Probability » Probability Generating Functions

Appeared in Year: 2014

### Describe in Detail

Let P (s) be the probability generating function associated with a non-negative, integer valued random variable X. Show that

### Explanation

To show this we use the left hand side, express the summation term

… (243 more words) …

## Question number: 4

» Probability » Probability Generating Functions

Appeared in Year: 2009

### Describe in Detail

Find the generating function of X whose probability density function is

P [X = r] =pq ^{r-1}, r = 1,2, …, 0 < p < 1, q = 1 - p

### Explanation

The probability generating function is defined as