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Suppose X Poi(X) for some positive X. a. Show that E(X) = X b. Show that E[X(X - 1)] = X².

Suppose X Poi(X) for some positive X. a. Show that E(X) = X b. Show that E[X(X - 1)] = X².

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem Statement:** Suppose \( X \sim Poi(\lambda) \) for some positive \(\lambda\). a. Show that \( E(X) = \lambda \). b. Show that \( E[X(X - 1)] = \lambda^2 \).
Transcribed Image Text:**Problem Statement:** Suppose \( X \sim Poi(\lambda) \) for some positive \(\lambda\). a. Show that \( E(X) = \lambda \). b. Show that \( E[X(X - 1)] = \lambda^2 \).
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