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Kalinka35
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Homework Statement
The location of an emergency is uniformly distributed over a city district. The district is a square rotated 45 degrees with "radius" r (the distance from the center to the top corner is r).
When the emergency occurs, the ambulance is at the center of the district. Let D be the "right-angle" distance from the ambulance to the emergency.
I need to find the cumulative distribution function FD(d) and the probability density function fD(d).
Homework Equations
The Attempt at a Solution
I know that the PDF is the derivative of the CDF so I am trying to find the CDF first.
It seems like you could define two random variables X and Y that give the coordinates of the emergency and the sum of those would give you the right-angle distance, but that seems like it might be overcomplicating things and you might just be able to work with D, the total distance.
Either way I just don't see how you can obtain a CDF.