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)