Question: The jurisdiction of a rescue team includes emergencies occurring on a stretch of river that is 4 miles long. Experience has shown that the distance along this stretch, measured in miles from its northernmost point, at which an emergency occurs can be represented by a uniformly distributed random variable. Then, if X = distance in miles from the northernmost point of this stretch of river.

a) Find and sketch the density function of this random variable.

b) Find and sketch the cumulative distribution function.

c) Find the probability that an accident occurs within one mile of the northernmost point of this stretch of river.

d) The rescues team’s base is at the midpoint of this stretch of river. Find the probability that a given emergency arises more than 1.5 miles from the base.