Probability-Probability Generating Functions (ISS 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

Essay Question▾

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

Equation

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

Equation

The generating function is

Equation<span class="more">… (56 more words) …</span>

Question number: 2

» Probability » Probability Generating Functions

Appeared in Year: 2009

Essay Question▾

Describe in Detail

Given the distribution function

Equation

find its probability density function.

Explanation

The distribution function written in this form

Equation

Equation

The density function is Equation

Equation

where Equation

Question number: 3

» Probability » Probability Generating Functions

Appeared in Year: 2014

Essay Question▾

Describe in Detail

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

Equation

Explanation

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

Equation

Equation

Equation

Equation

Equation

Equation

We know that the probability generating function is defined as

Equation

Putting this in the above equation, we prove the following

Equation

Question number: 4

» Probability » Probability Generating Functions

Appeared in Year: 2009

Essay Question▾

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

Equation

Equation

Equation

Equation

Equation

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