Let Y1=0+e1and then for t>1 define Yt recursively by Yt=0+Yt1+et. Let e1,e2,... be a sequence of independent, identically distributed random noises each with zero mean and variance e2. Here 0 is a constant. The process {Yt} is called a random walk with drift.

(1) Show that Yt may be rewritten as Yt=t0+et+et1++e1.

(2) Find the mean function for Yt.

(3) Find the autocovariance function for Yt.

-Let Y1 = 60 + 31 and then fort > 1 define Y, recursively by K = 90 + 12.1 + 3;. Let a] , {-32, be a sequence of independent, identically distributed random noises each with zero mean and variance 0'3. Here 60 is a constant. The process {K} is called a random walk with drift. [1} Show that 1'} may be rewritten as 1'} = 1'90 +6; + 6H + +621. [2) Find the mean function for K. (3) Find the autocouariance function for K