Consider a small network where data packets are sent from a client to a server through a

single router. The router has a buffer that can hold a maximum of $10$ packets. When the

buffer is full, any additional packets that arrive are dropped, resulting in packet loss.

Packets arrive at the router at an average rate of $12$ packets per second, but the router can

only process $10$ packets per second.

$($a$)$ Calculate the packet loss rate per second at the current processing rate.

$($b$)$ If the router$$s processing rate was increased to $15$ packets per second, how would it

impact the packet loss rate?