Let nodes $L$ and $M$ be on the same broadcast channel using $CSM\frac{A}{C}D,$ and let the propagation delay between the two nodes be $400$ bit times. Suppose node $L$ starts transmitting a $900-$bit frame at time $t=0,$ and node $M$ begins transmitting a frame sometime after that. Use one bit time as the unit of time for your answers.

$($a$)$ What is the range of times that $M$ can start transmitting such that $L$ will detect a collision before it finishes transmitting its frame? Explain.

$($b$)$ Is there the range of times that $M$ can start transmitting such that a collision occurs, but $L$ will not detect a collision before it finishes transmitting its frame? Explain.

$($c$)$ What is the earliest that $M$ can start transmitting such that no collision will occur?

Explain.