In hyde park there are six taxi companies. when you call company #1, the amount of time (in minutes) that it takes the cab to arrive is distributed as exponential(1); if you call company #2, then it's distributed as exponential(2), if you call company #6, it's generated as exponential(6). (recall that an exponential(a) distribution, whose parameter is the rate 1, has mean 1/1 and variance 1/12.) a statistician rolls a single standard die (sides numbered 1,2,3,4,5,6), and looks at the number rolled (let's call it x). next, she calls the company chosen by the roll of the die. let t be the amount of time that she waits for a cab to arrive. you are waiting for the cab with her, but you don't know what was the roll of the die. (a) write down a hierarchical model. (b) calculate p(t > t) where t is a fixed value. (c) calculate e(t). (d) suppose that after t minute the cab has not yet arrived. given this information, what is the conditional distribution of x? (e) as t goes to infinity, describe how the conditional distribution of x changes. which taxi companies become more/less likely? (hint: you may want to calculate explicit probabilities at a few values of t—but this is not necessary.)