document.write( "Question 1155063: The following density function describes a random variable 𝑋.
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Algebra.Com's Answer #777663 by Edwin McCravy(20077)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Its graph is this:\r\n" );
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document.write( "In order for it to be a probability density function, it must be such that when\r\n" );
document.write( "we shade the area between it and the x-axis, that area must be exactly 1.\r\n" );
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document.write( "It's a probability density function because the area between it and the x-axis\r\n" );
document.write( "is a triangle whose base is 4 and whose height is 1/2 or 0.5 since when we\r\n" );
document.write( "substitute x=5 in (𝑥−1)/8 we get 4/8 or 1/2 or 0.5 and the area of a triangle is\r\n" );
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document.write( "\"A=expr%281%2F2%29base%2Aheight=expr%281%2F2%29%284%29%281%2F2%29+=+1\"\r\n" );
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document.write( "Since the entire area between the graph and the x-axis is 1, it is indeed a\r\n" );
document.write( "probability density function.  So the problem was telling the truth when it said\r\n" );
document.write( "this is a probability density function.\r\n" );
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document.write( "The probability that 𝑋 is between two values is the area between the graph and\r\n" );
document.write( "the x-axis between those two values.\r\n" );
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A. Find the probability that 𝑋 lies between 2 and 4.
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document.write( "This asks for the area between 2 and 4, which is this shaded area:\r\n" );
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document.write( "This is a trapezoid (or 'trapezium' if you live in the UK), and if you turn your\r\n" );
document.write( "head 90° it has two bases b1=0.125 and b2=0.25, and \r\n" );
document.write( "height = 2.  The formula for the area is\r\n" );
document.write( "\"A=expr%281%2F2%29%28b%5B1%5D%2Bb%5B2%5D%29h=%280.5%29%280.125%2B0.375%29%282%29+=+0.5=1%2F2\" \r\n" );
document.write( "So that's  the answer.\r\n" );
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B. Find the probability that 𝑋 is less than 3.
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document.write( "the shaded area between between the graph the x-axis is a triangle whose base is\r\n" );
document.write( "2 and whose height is 1/4 or 0.25 since when we substitute x=2 in (𝑥−1)/8 we get\r\n" );
document.write( "1/8 or 0.125 and the area of a triangle is \r\n" );
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document.write( "\"A=expr%281%2F2%29base%2Aheight=expr%281%2F2%29%282%29%281%2F4%29+=+1%2F4+=+0.25\"\r\n" );
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document.write( "That's the answer.\r\n" );
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document.write( "Edwin

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