1. If x and y are statistically independent, then E[xy] = E[x]E[y]. That is, the expected value of the product xy is equal to the product of the separate mean values. If z = x + y, where x and y are...

1. If
x
and
y
are statistically independent, then
E[xy] =
E[x]E[y]. That is, the expected value of the product
xy
is equal to the product of the separate mean values. If
z
=
x
+
y, where
x
and
y
are statistically independent,

show that
E[z
²] =
E[x
²] +
E[y
²] + 2E[x]E[y].

2. Find the autocorrelation functions of the periodic functions shown in Fig. 14.24.