Please help me with this Homework problem, and please explain on how to do them

Question

Please help me with this Homework problem, and please explain on how to do them

A women falls asleep while riding a bus. The bus travels at a constant speed along a route that includes her house. The endpoints of the route are 2 miles east and 3 miles west of her house. An accident occurs which causes her to pull over. Assume that this occurs at uniformly random positon along the route.

a. What is the probability that she is west of her house when she awakes?

b. What is the probability that she is at least 1.5 miles from her house when she awakes?

c. What is the expected distance from her house when she awakes? Note that distances are always non-negative.

d. The woman's house is equipped with a supercharged wi-fi signal booster whose strength decays quadratically with distance. In particular, if she is D miles from home, she is able to recieve (100/(1+D)^2) Megabits/sec; for example, at home D=0, and the signal is at its maximum speed of 100 megabit/sec. if video streaming requires at least 16 megabits/sec, what is the probability that she will be able to watch a video as she waits for the bus to be repaired?

Explanation / Answer

A) P(West of her house) = 3/(3+2) = 0.6

B) P(at least 1.5 miles from her house) = p(1.5 mile east) + P(1.5 mile west)

= (1.5 + 1.5)/5

= 0.6

C) Expected distance = (3+2)/2 - 2

= 2.5 - 2

= 0.5 miles

D) For 16mbps, maximum D possible

= 100/(1+D)2 = 16

D = 1.5

P(she will be able to watch the video) = P(within 1.5km from house)

= 0.6

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