$2.$ A video streaming service uses UDP for transmitting video packets. The service transmits video data at a rate of $2$ Mbps to a user located $1000$ km away. The propagation delay on the network is $5$ milliseconds per kilometer. The user's buffer can store up to $2$ seconds of video data. Determine:

a$.$ The total end$-$to$-$end delay experienced by the user for receiving a video packet.

b$.$ The minimum buffer size required at the user's end to avoid buffer underflow.

c$.$ If the user's buffer size is increased to $4$ seconds, how does it affect the quality of video streaming?