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2. Suppose that X and Y are independent random variables, both with the standard normal distribution i.e. X, Y~ N(0, 1). For pe [-1, 1], define √1-p²X + pY. Show that E[ZY] = pY. Z:=

2. Suppose that X and Y are independent random variables, both with the standard normal distribution i.e. X, Y~ N(0, 1). For pe [-1, 1], define √1-p²X + pY. Show that E[ZY] = pY. Z:=

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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2. Suppose that X and Y are independent random variables, both with the standard normal distribution i.e. X, Y~ N(0, 1). For pe [-1, 1], define Z:=√1-p²X + pY. Show that E[Z|Y] =pY.
Transcribed Image Text:2. Suppose that X and Y are independent random variables, both with the standard normal distribution i.e. X, Y~ N(0, 1). For pe [-1, 1], define Z:=√1-p²X + pY. Show that E[Z|Y] =pY.
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