my take:
Rvv = E{w(t1)*cos(2Πft1+Φ) * w(t2)*cos(2Πft2+Φ)}
since w and Φ are indep,
Rvv = E{w(t1) * w(t2)} * E{cos(2Πft1+Φ) * cos(2Πft2+Φ)}
first term =1 , assuming w has unit power
Rvv = E{cos(2Πf ((t1+t2) + 2Φ) * cos(2Πf(t1-t2))} * 1/2
first term evaluates to zero, assuming Φ is uniformily didstibuted between 0 and 2Π, second terms is deterministic.
Rvv(ζ) = cos(2Πfζ) * 1/2
-b
Added after 7 minutes:
but since w is given as white,
E{w(t1) * w(t2)} = 1 only when t1 = t2 and 0 else.
So then,
Rvv = 1/2
comments?
-b