Suppose a bus arrives at a station such that the time between arrivals is exponentially distributed with rate 1/λ. to get home, you decide to wait for the bus for some number of minutes t. if the bus has arrived before t minutes, you take the bus home which takes time b. if the bus has not arrived after t minutes, you walk home which takes time w.

(a) what is the expected total time from getting to the bus stop until getting home?

(b) suppose w < 1/λ + b at what value of t is the expected wait time minimized?

(c) suppose w > 1/λ + b at what value of t is the expected wait time minimized?

Michelle and julie work at a catering company. they need to bake 264 cookies for a birthday party that starts in a little over an hour and a half. each tube of cookie dough claims to make 36 cookies, but michelle eats about 1/5 of every tube and julie makes cookies that are 1.5 times as large as the recommended cookie size. it takes about 8 minutes to bake a container of cookies, but since julie's cookies are larger, they take 12 minutes to bake. a. how many tubes should each girl plan to bake? how long does each girl use the oven? b. explain your solution process what did you make? c. what assumptions did you make?

Kevin's bank offered him a 4.5% interest rate for his mortgage. if he purchases 3 points, what will be his new rate?

Hundred and tens tables to make 430 in five different ways