Hand in: Refer to Example C pg 117 (Rice). Show that E-0 xp(x) = 1 if X~Poi(1). Expand the steps. %3D 2x=0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.4: Logarithmic Functions
Problem 45E
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Hand in: Refer to Example C pg 117 (Rice). Show that E=0 xp(x) = 1 if X~Poi(2). Expand
the steps.
Transcribed Image Text:Hand in: Refer to Example C pg 117 (Rice). Show that E=0 xp(x) = 1 if X~Poi(2). Expand the steps.
EXAMPLEC
Poisson Distribution
The expected value of a Poisson random variable is
k入
E(X) = )
k!
入ペー!
= le)
(k 1)!
Σ
j!
= de-
Since (A/j!) = e, we have E(X) = À. The parameter À of the Poisson
distribution can thus be interpreted as the average count.
Transcribed Image Text:EXAMPLEC Poisson Distribution The expected value of a Poisson random variable is k入 E(X) = ) k! 入ペー! = le) (k 1)! Σ j! = de- Since (A/j!) = e, we have E(X) = À. The parameter À of the Poisson distribution can thus be interpreted as the average count.
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