Thread: Conditional distribution and finding unconditional distribution

Stuck on this one... feel like I should know it

Y and Z are univariate r.v. such that

Y|Z=z ~ N(a+z,sigma^2) , Z ~ N(0,lamda^2)

Find the unconditional dist of Y

Find the unconditional (joint) dist of Y1,... Yn following the above with Yi|Z=z ~ N(ai+z,sigma^2)

Originally Posted by statstian

Stuck on this one... feel like I should know it

Y and Z are univariate r.v. such that

Y|Z=z ~ N(a+z,sigma^2) , Z ~ N(0,lamda^2)

Find the unconditional dist of Y

Find the unconditional (joint) dist of Y1,... Yn following the above with Yi|Z=z ~ N(ai+z,sigma^2)

Will the approach be similar to here: http://www.mathhelpforum.com/math-he...ease-help.html .... ?

Yes that is the approach I took. But I got lost doing the intergral.

All the variables and algebra had me thinking I made a mistake.

Thanks