Suppose your waiting time for a bus in the morning is uniformly distributed on $[0,10],$ whereas waiting time in the evening is uniformly distributed on $[0,12]$ independent of morning waiting time.

$($a$)$

If you take the bus each morning and evening for a week, what is your total expected waiting time? $($Assume a week includes only Monday through Friday.$)[$Hint: Define rv$\text{'}$s

X$1,,$ X$10$

and use a rule of expected value.$]$