Q$1)(25$p$)$ Six received power measurements were taken at different distances from a transmitter. The received power measured are shown in the following table. It is assumed that the path loss for these measurements follows the model.

$PL(d)[dB]\frac{?}{b}=ar(PL(d))+x_{}\frac{?}{b}=ar(PL(d_0))+10nlog(\frac{d}{d_0})+x_{}$

where $d_0=100m.$

$\backslash$table$[[$Distance $(km),0\mathrm{.}1,0\mathrm{.}2,1,2,4,10],[$Power $(dBm),0,-9\mathrm{.}5,-34,-47,-55,-72]]$

$($a$)$ Find the estimate for the path loss exponent, n with minimum mean square error $($MMSE$).$

$($b$)$ Calculate the standard deviation of shadowing about the mean value.

$($c$)$ Estimate the received power at $d=8km$ using the resulting model.

$($d$)$ Predict the likelihood that received signal level at $10$ km will be greater than $-72$ dBm $.$

$($e$)$ Predict the percentage of area within a $10$ km radius cell that the receives signal greater than $-72$ dBm $.$