Let X 1 ,X 2 ,... be a sequence of zero-mean, independent, identically distributed random variables with variance  Define   Prove that   is non-stationary by computing r Y (1,2) and r Y (2,3). The...

Let X₁,X₂,... be a sequence of zero-mean, independent, identically distributed random variables with variance
 Define

Prove that
  is non-stationary by computing r_Y(1,2) and r_Y(2,3). The non-stationarity can be corrected by letting Y₁
= cX₁
for an appropriate choice of the constant c. Find such a c.