(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given a unit square and a 'target' square of size LXL = p^2 < 1 in the unit square. The center of target square in equally likely to be anywhere in the unit square. What is the average size of the target square as a function of p^2.

This is the problem and I have included a jpeg illustration of the problem. Any help would be greatly appreciated.

My attempt at the problem :

I divided the problem into three cases : one where the target square is completely in the unit square : one where half the target square is in the unit square and one where quarter of the target square is in the unit square. I then calculated the expectation integral of p^2 but I am confused as to what the probability density function is and what the limits of integral are for each of the cases.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Expected value of area

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**