Question

Consider a road that is 93 kilometres long. You meet with an accident at a point which is uniformly distributed on the road. An ambulance is waiting at a location on the road, which is also uniformly distributed. It is safe to assume that these two random variables are independent. What is the expected distance between you and the ambulance at the time of the accident?

Answer 1

Let X be a distance at which the accidents occur.
Let Y be a distance at which the ambulance is standing.

It is given that,



Let Z be the distance between the accidents occur and the ambulance is standing.

Now,

Now,

Now,

















Hence,




Hence, the expected distance between you and the ambulance at the time of the accident is 0.

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