Suppose that x$\_($i$)$N$(\backslash$mu $,\backslash$sigma $^(2)),$i$=1,$dots,n and Z$\_($i$)$N$(0,1),$i$=1,$dots,k$,$ and all variables are independent. State the distribution of each of the following variables if it is a "named" distribution or otherwise state "unknown." $($a$)$ x$\_(1)-$x$\_(2)($i$)($Z$\_(1)^(2))/($Z$\_(2)^(2))($b$)$ x$\_(2)+2$x$\_(3)($j$)($Z$\_(1))/($Z$\_(2))($c$)($x$\_(1)-$x$\_(2))/(\backslash$sigma S$\_($Z$)\backslash$sqrt$(2))($k$)((\backslash$bar$\{$x$\}))/(/$bar $(/$bar $($Z$)))($d$)$ Z$\_(1)^(2)($l$)(\backslash$sqrt$($nk$)((\backslash$bar$\{$x$\})-\backslash$mu $))/(\backslash$sigma $\backslash$sqrt$(\backslash$sum$\_($i$=1)^$k Z$\_($i$)^(2)))($e$)(\backslash$sqrt$($n$)((\backslash$bar$\{$x$\})-\backslash$mu $))/(\backslash$sigma S$\_($z$))($m$)(\backslash$sum$\_($i$=1)^$n $($x$\_($i$)-\backslash$mu $)^(2))/(\backslash$sigma $^(2))+\backslash$sum$\_($i$=1)^$k $($Z$\_($i$)-(/$bar $($Z$)))^(2)($f$)$ Z$\_(1)^(2)+$Z$\_(2)^(2)($n$)((\backslash$bar$\{$x$\}))/(\backslash$sigma $^(2))+(\backslash$sum$\_($i$=1)^$k Z$\_($i$))/($k$)($g$)$ Z$\_(1)^(2)-$Z$\_(2)^(2)($o$)($k$)/($b$)$ar $($Z$)^(2)($h$)($Z$\_(1))/(\backslash$sqrt$($Z$\_(2)^(2)))($