X and Y are i.i.d random variables with Poisson distribution with parameter d and A2, pectively. If the random variables Z, and Z2 are defined as: Z, = X + 2Y and Z2 = 2X + Y, Find E{X|Z1)? Find E(Z,Z,)?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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P7. X and Y are i.i.d random variables with Poisson distribution with parameter 1, and A2,
respectively. If the random variables Z, and Z2 are defined as: Z, = X + 2Y and Z2 = 2X + Y,
a. Find E{X|Z1)?
b. Find E (Z,|Z2)?
c. What is joint characteristic function between X and Y?
d. If 11 = 12, find joint characteristic function between Z, and Z2?
%3D
Transcribed Image Text:P7. X and Y are i.i.d random variables with Poisson distribution with parameter 1, and A2, respectively. If the random variables Z, and Z2 are defined as: Z, = X + 2Y and Z2 = 2X + Y, a. Find E{X|Z1)? b. Find E (Z,|Z2)? c. What is joint characteristic function between X and Y? d. If 11 = 12, find joint characteristic function between Z, and Z2? %3D
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