# The jurisdiction of a rescue team includes emergencies occurring on a stretch of river that is 4

## 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 over the range 0 to 4 miles. Then, if X denotes the distance (in miles) of an emergency from the northernmost point of this stretch of river, its probability density function is as follows:

a. Graph the probability density function.
b. Find and graph the cumulative distribution function.
c. Find the probability that a given emergency arises within 1 mile of the northernmost point of this stretch of river.
d. The rescue 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 this base.

Distribution
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