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▾

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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

P(z)=n=0znpn

(i) The generating function of Pr [X > n] is… (475 more words) …

Question number: 2

» Probability » Probability Generating Functions

Appeared in Year: 2009

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Given the distribution function

F(x)=12+x2(1+ x )<x<

find its probability density function.

Explanation

The distribution function written in this form

F(x)={12+x2(1+x);0<x<12x2(1+x);<x<0

F(x)… (98 more words) …

Question number: 3

» Probability » Probability Generating Functions

Appeared in Year: 2014

Essay Question▾

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

n=0snP(Xn)=P(s)1s

Explanation

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

n=0snP(Xn)=P(X0)+sP(X1)+s2P(X2)… (352 more words) …

Question number: 4

» Probability » Probability Generating Functions

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

E(tz)=z=1tzP[X=z]

=z=1tzpqz1

=ptz=1[tq… (28 more words) …

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