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

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Appeared in Year: 2013

Essay Question▾

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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

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Appeared in Year: 2009

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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

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Appeared in Year: 2014

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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

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Appeared in Year: 2009

Essay Question▾

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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

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