document.write( "Question 1151395: If the random variable X has uniform distribution on the interval [0,a] then
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Algebra.Com's Answer #773159 by ikleyn(52908) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "1)  First, let's consider the case  a < 1.\r\n" );
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document.write( "    Then for all values of x in the segment [0,a]  x > x^2  (which is ABSOLUTELY OBVIOUS).\r\n" );
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document.write( "    So, if a < 1, then  P(x > x^2) = 1.\r\n" );
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document.write( "2)  Next, consider the case a >= 1.\r\n" );
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document.write( "    Then x > x^2 if and only if  0 <= x < 1.\r\n" );
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document.write( "    Therefore, P(x > x^2) =   ( since the random variable x has uniform distribution on the interval  [0,a]).\r\n" );
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document.write( "3)  Thus the final ANSWER / (the final formula) is THIS :\r\n" );
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document.write( "    if the the random variable X has uniform distribution on the interval [0,a] then\r\n" );
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document.write( "        the probability that the random variable is greater than its square, i.e.  P(x > x^2),  is equal to  1,  if a < 1\r\n" );
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document.write( "    and\r\n" );
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document.write( "        the probability that the random variable is greater than its square, i.e.  P(x > x^2),  is equal to  ,  if a >= 1.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Notice, I edited my post after receiving a note from Edwin.\r
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\n" ); document.write( "\n" ); document.write( "What you see now in my post is the final version.\r
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\n" ); document.write( "\n" ); document.write( "Thanks to Edwin for his note.\r
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