Suppose y is the number of in volume v and assume that y follows the poisson distribution with mean λv. a. if a point is randomly selected within the volume v find the pdf of its distance r from the nearest pollution particle. note the volume of a sphere with radius r is 4 3 πr3 . b. refer to question (a). let u = r3 . show that u follows exponential distribution. what is the mean and variance of u?

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?