$$4\mathrm{.}4$ #$63.$ A consumer is trying to decide between two long$-$distance calling plans. The first one

charges a flat rate of $10c$ per minute, whereas the second charges a flat rate of $99c$ for calls up

to $20$ minutes in duration and then $10c$ for each additional minute exceeding $20($assume that

calls lasting a non$-$integer number of minutes are charged proportionately to a whole$-$minute's

charge$).$ Suppose the consumer's distribution of call duration is exponential with parameter $.$

Write out the cost formula for each plan as a function of call duration $x,$ and compute the

expected cost $($as a function of parameter $)$ respectively $(cost=f(x),$ so $E[cost]=E[f(x)],$ which

is a function of lambda$).$

cost of plan I $($as a function of $x)=$

cost of plan II $=$

E$[$cost of plan I$]=$

E$[$cost of plan II$]=$