depending on the condition of the radio channel between a laptop and an access point. The speeds are high $(h)$ at $54M\frac{b}{s},$ medium $(m)$ at $11M\frac{b}{s},$ and low $(l)$ at $1M\frac{b}{s}.$ A user of the wi$-$fi connection can transmit a short signal corresponding to a mouse click $(c),$ or a long signal corresponding to a tweet $(t).$ Consider the experiment of monitoring wi$-$fi signals and observing the transmission speed and the length. An observation is a two$-$letter word, for example, a high$-$speed, mouse$-$click transmission is hm$.$

$($a$)$ What is the sample space of the experiment?

$($b$)$ Let $A_1$ be the event "medium speed connection." What are the outcomes in $A_1?$

$($c$)$ Let $A_2$ be the event "mouse click." What are the outcomes in $A_2?$

$($d$)$ Let $A_3$ be the event "high speed connection or low speed connection." What are the outcomes in $A_3?$

$($e$)$ Are $A_1,A_2,$ and $A_3$ mutually exclusive?

$($f$)$ Are $A_1,A_2,$ and $A_3$ collectively exhaustive?