yeah, I got that.
and 0.2375,0.2235,0.1341 for rest of three questions respectively.

My understanding of filter representations is that it's used to estimate the variance of forecast.  We can convert the φ parameters into an infinite series of θ parameters.  This is helpful because the θ parameter only changes one period in the future.  I'm anticipating that the final might ask, "What is the variance of the one period ahead forecast?  Two?  Three?" 

There's a few practice problems in the Module 7 Stationary mixed processes that might be helpful in understanding the concepts.

[NEAS: Correct; the filter representation converts an autoregressive processes into a moving average model of infinite rank. This simplifies the formulas for the variance of forecasts because all the error terms are independent, whereas the observations are serially correlated.]

I'm blanking, what is Filter Representation?

Also, I got the same answer as above for the first problem.  As to the "crazy" amount of algebra, the formulae on page 78 (4.4.3-5) made this assignment take a couple minutes. 

RDH

I used filter representation and first principles so memorizing formulas was not necessary.

did anyone get 1.0625 for the first question?

this is a crazy amount of algebra if you don't have the formulas for these memorized. are there lots of these on the test? any of these? are formulas given? sheesh.