MMSE predictor and interpolator. A scalar time series x(0), x(1),... is modeled as a moving average (MA) process:

x(t) = a₀w(t) + a₁w(t-1) + a₂w(t-2) +... +a_Nw(t-N).

where w(t) are i.i.d. N(0,1).Assume that the coefficients a₁, a₂,... a_N, are known.

a)Predicting the next value from the current value.Find the MMSE predictor of x(t+1) based on x(t).(Note, based just on x(t), not on x(t-1), x(t-2), ...).

b)MMSE interpolator.Find the MMSE predictor of x(t) based only on x(t-1) and x(t+1).