1.) Suppose (z₁,z₂)~BVN(4,3,16,9,0.5) calculate:

a) E(0.5Z₁+(1/3)Z₂)

b) Cov(Z₁,Z₂)

c) Var(Z₁+Z₂)

d) Var(7+5Z₁-2Z₂)

e) Cov(Z₁-Z₂,Z₁+Z₂)

f) Cov(1+Z₂-3Z₁,Z₁+2Z₂)

My answers:

a) 3

b)6

c)37

d)316

e)7

f)-60

2.) let {at} be a zero-mean white noise process with variance sigma_a²

determine the autocorrelation function for:

Yt=a_t+(1/3)a_t-1

X_t=a_t+3a_t-1

My answer:

p_t,t+k=3/10 for k=-1,1 and p_t,t+k=1 for k=0 in both the case of Y_t and X_t.

Are my answers correct if not please help me with the equations?