Question 462754: choose a point randomly from the unit square.Let X denote the distance of the chosen point from the closest side of the square.find the means and standard dieviation of X
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! The set of all points at a certain distance x from an edge of the square, where  , can be thought of as the area bordering the square of thickness x (from the inside of the square, not on the outside). Then the area of the inner square is  , and the area around the square (which is the area we wanted) is  .
The probability that a point is LESS THAN OR EQUAL TO x units from an edge is given by
 , where .
This the cdf. To get the pdf f(x), take the derivative of F(x), so
f(x) = 4 - 8x, where, . (Check quickly that indeed this is a valid pdf by integration from 0 to 1/2.)
Now 
Also, 
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