if Z1 and Z1 are r.v with distribution N(0,1) and X1,X2 are r.v

and X1 = a + bZ1 and X2 = c + dZ1 + eZ2

then to calculate E[X2|X1=x1] can we just rearange and substitute so

E[X2|X1=x1] = E[c + d((x1 -a)/b) + eZ2] = c + (d/b)E[X1] - a/b

= c+ a/b(d-1)

thanks