(a) Let U be an n-rv with mean m and covariance [K] whose MGF is given by (3.18). Let X = rT U for an arbitrary real n-vector r. Show that the MGF of X is given by gX (r) = exp rrE [X] + r2σ 2/2l...

(a)
Let

U

be an
n-rv
with mean

m

and covariance [K] whose MGF is

given by (3.18). Let
X
=
rT

U

for an arbitrary real
n-vector

r
. Show that the MGF of
X
is given by gX
(r) = exp rrE [X] +
r2σ

2/2l and relate E [X] and
σ
2 to

m

and [K].

X
X

(b)
Show that

U

is a Gaussian rv.