$($i$)(5\%)$ Find the differential entropy in bits of a Gaussian random variable with mean $0$ and

variance $1$; find the differential entropy in bits of a Gaussian random variable with mean $10$

and variance $1.$

$($ii$)(10\%)$ Find the joint differential entropy in bits h$($X$1,$ X$2)$ of two jointly Gaussian random

variables X$1,$ X$2$ with autocorrelation matrix R $=$

$[10\mathrm{.}1$

$0\mathrm{.}11$

$]$

$.$ Next, find h$($X$1|$ X$2).$

$($iii$)(5\%)$ For the random variables in Part $($ii$),$ how much is I$($X$1$; X$2)$