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I am confused by such a conditional expectation problem:
A normal random variable Z~N(u,s² ) is added by two identically distributed but independent random variables Z[sub]1[/sub] & Z[sub]2[/sub], that is to say, both have expectation u/2, and variance s²/2.
Here comes the problem:
Pr(Z[sub]1[/sub]=x|Z=y)=?
Thank you.
X'(y-Xβ)=0
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Let me see,
f(z)=f1(z1)f2(z2) where f(z)=d[Pr(Z<z)]/dz
The event Z=y means Z1+Z2=y or Z2=y-Z1
The density of the event Z=y
would be integration of f1(z1)f2(y-z1) from z=-∞ to z=+∞
and what next?
X'(y-Xβ)=0
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