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#1 2009-08-22 00:00:47

George,Y
Member
Registered: 2006-03-12
Posts: 1,379

Conditional Probability distribution

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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#2 2009-08-22 00:12:51

George,Y
Member
Registered: 2006-03-12
Posts: 1,379

Re: Conditional Probability distribution

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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