Lecture 9_13

The variance of zt around its expected value E( gt ) in this particular generation is σ g(t) + σ 2 e(t). However, we usually don’t know the particular value of dt, which is assumed to be uncorrelated between generations (σ(dt, dt′) = 0), with mean 0 and variance σ d. Thus, the expected value of zt measured at a random time (e.g., the value of d is chosen at random) is μ+E( gt ) and the variance of zt about this mean value is inflated by σ d to give σz(t) = σ 2 g(t) + σ 2 e(t) + σ 2 d (9.3)