$4.(20$ pts$.)$ Use the master method to give tight asymptotic bounds for the following recurrences:

$($a$)$ Tpnq $2$Tpn$\{4$q $`1$

$($b$)$ Tpnq $2$Tpn$\{4$q $`$ n

$($c$)$ Tpnq $2$Tpn$\{4$q $`$ n$2$

$($d$)$ Tpnq $2$Tpn$\{4$q $`$ n$1\{2$