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Recurrence times are insensitive to distributions. Let XO, X1, X2, ... be drawn i.i.d. p(x), X E X = {1, 2,...,m}, and let N be the waiting time to the next occurrence of XO. Thus N = min n{Xn = XO). (a) Show that EN = m. (b) Show that E log N≤ H (X). (c) (Optional) Prove part (a) for (Xi) stationary and ergodic.

Recurrence times are insensitive to distributions. Let XO, X1, X2, ... be drawn i.i.d. p(x), X E X = {1, 2,...,m}, and let N be the waiting time to the next occurrence of XO. Thus N = min n{Xn = XO). (a) Show that EN = m. (b) Show that E log N≤ H (X). (c) (Optional) Prove part (a) for (Xi) stationary and ergodic.

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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Recurrence times are insensitive to distributions. Let XO, X1, X2, ... be drawn i.i.d. - p(x), x eX = {1, 2,...,m}, and let N be the waiting time to the next occurrence of XO. Thus N = min n{Xn = XO). (a) Show that EN = m. (b) Show that E log N< H (X). (c) (Optional) Prove part (a) for {Xi} stationary and ergodic.
Transcribed Image Text:Recurrence times are insensitive to distributions. Let XO, X1, X2, ... be drawn i.i.d. - p(x), x eX = {1, 2,...,m}, and let N be the waiting time to the next occurrence of XO. Thus N = min n{Xn = XO). (a) Show that EN = m. (b) Show that E log N< H (X). (c) (Optional) Prove part (a) for {Xi} stationary and ergodic.
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