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Example 7:36. Let (X₁) be mutually independent, each assuming the values 0, 1, 2, 3, ..., a – 1 with probability /. Let Sn = X₁ + X₂ + ... + X,. Show that the probability generating function of Sn is : and hence P (s) = { 1-s a(1- P (Sn = j) = -—- Σ (− 1)v+j+ªv (") (₁ =7) av v=0

Example 7:36. Let (X₁) be mutually independent, each assuming the values 0, 1, 2, 3, ..., a – 1 with probability /. Let Sn = X₁ + X₂ + ... + X,. Show that the probability generating function of Sn is : and hence P (s) = { 1-s a(1- P (Sn = j) = -—- Σ (− 1)v+j+ªv (") (₁ =7) av v=0

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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8/ Example 7-36. Let {Xg} be mutually independent, each assuming the values 0,1.2 3 ..., a – 1 with probability Let S„ = X1 + X2 + ... + Xp. Show that the probability generating P (s) = { 6)= { 1-s a(1 – s) function of S, is : P (S„ = j) =£ (-1)**jtev (") (;="av) and hence V=0
Transcribed Image Text:8/ Example 7-36. Let {Xg} be mutually independent, each assuming the values 0,1.2 3 ..., a – 1 with probability Let S„ = X1 + X2 + ... + Xp. Show that the probability generating P (s) = { 6)= { 1-s a(1 – s) function of S, is : P (S„ = j) =£ (-1)**jtev (") (;="av) and hence V=0
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