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 #773157 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Uniform distribution means the distribution is a rectangle over\r\n" );
document.write( "the interval [0,a] whose area is 1. The base of the rectangle is\r\n" );
document.write( "the interval from 0 to a, so the base of the rectangle is \"a\" units.\r\n" );
document.write( "Let its height be h.\r\n" );
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document.write( "Area = base∙height\r\n" );
document.write( "   1 = a∙h\r\n" );
document.write( " 1/a = h\r\n" );
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document.write( "We need to locate a place on that graph where\r\n" );
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document.write( "\"x%3Ex%5E2\"\r\n" );
document.write( "\"x%5E2%3Cx\"\r\n" );
document.write( "\"x%5E2-x%3C0\"\r\n" );
document.write( "\"x%28x-1%29%3C0\"\r\n" );
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document.write( "Since x is positive, x-1 must be negative,\r\n" );
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document.write( "\"x-1%3C0\"\r\n" );
document.write( "\"x%3C1\"\r\n" );
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document.write( "So we locate 1 somewhere on that graph:\r\n" );
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document.write( "and we shade the area under the rectangle to the left of 1, since it's x < 1:\r\n" );
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document.write( "The area of that shaded part, which has base 1 and height 1/a is\r\n" );
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document.write( "Area = base × height = 1 × 1/a = 1/a\r\n" );
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document.write( "That's the answer: the probability is 1/a.\r\n" );
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document.write( "Edwin
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