document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #317315 by robertb(5830) $\"\"$ $\"About$

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The set of all points at a certain distance x from an edge of the square, where $\"0+%3C=+x+%3C=+1%2F2\"$ , 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 $\"%281-2x%29%5E2\"$ , and the area around the square (which is the area we wanted) is $\"1+-+%281-2x%29%5E2+=+4x+-+4x%5E2\"$ .\r
\n" ); document.write( "\n" ); document.write( "The probability that a point is LESS THAN OR EQUAL TO x units from an edge is given by \r
\n" ); document.write( "\n" ); document.write( " $\"F%28x%29+=+P%28X+%3C=+x%29+=+4x+-+4x%5E2\"$ , where $\"0+%3C=+x+%3C=+1%2F2\"$ .\r
\n" ); document.write( "\n" ); document.write( "This the cdf. To get the pdf f(x), take the derivative of F(x), so
\n" ); document.write( "f(x) = 4 - 8x, where, $\"0+%3C=+x+%3C=+1%2F2\"$ . (Check quickly that indeed this is a valid pdf by integration from 0 to 1/2.)\r
\n" ); document.write( "\n" ); document.write( "Now

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\n" ); document.write( "==> $\"sigma%5E2+=+E%28X%5E2%29+-+mu%5E2+=+1%2F24+-+1%2F36+=+1%2F72\"$ \r
\n" ); document.write( "\n" ); document.write( "==> $\"sigma+=+1%2F%286sqrt%282%29%29\"$ \n" ); document.write( "

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