document.write( "Question 1168707: A random variable X has pdf f(x) = (3/4)(1-x^2) from -1 < x < 1. \r
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\n" ); document.write( "\n" ); document.write( "I have found that the cdf = F(x) = -(x^3)/4 + 3x/4
\n" ); document.write( "by taking the integral of f(t) = (3/4)(1-t^2) from [-1,x]\r
\n" ); document.write( "\n" ); document.write( "From there I know I need to solve for F(x) = 0.25, F(x) = 0.5 and F(x) = 0.75. However when I solve for those, I keep getting values outside of the interval [-1,1]. \n" ); document.write( "

Algebra.Com's Answer #793315 by ikleyn(52777) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "The pdf function is  f(x) =   on the interval  [-1,1].\r\n" );
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document.write( "The cdf function is  antiderivative  F(x)  of  f(x)  such that F(-1) = 0.\r\n" );
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document.write( "So, the antiderivative is  F(x) =  =  -  + ,     (1)\r\n" );
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document.write( "where C is the constant such that  F(-1) = 0.\r\n" );
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document.write( "From this condition,  you have this equation, substituting x= -1 into the formula (1) \r\n" );
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document.write( "     -  +  = 0,    or\r\n" );
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document.write( "     = 0,                  or\r\n" );
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document.write( "     = 0,\r\n" );
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document.write( "which gives\r\n" );
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document.write( "    C = .\r\n" );
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document.write( "So, your antiderivative, or cdf function is\r\n" );
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document.write( "    F(x) =  -  + .\r\n" );
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document.write( "Thus I complete calculating the needed cdf function.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Now my short COMMENT regarding your solution.\r
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document.write( "    Your solution was INCORRECT.\r\n" );
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document.write( "    You incorrectly found the cdf function,\r\n" );
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document.write( "    because in integrating process you forgot about the constant term \"C\"\r\n" );
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document.write( "                                   and forgot to satisfy the condition F(-1) = 0 for your cdf function.\r\n" );
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\n" ); document.write( "\n" ); document.write( "I stop at this point leaving to complete the part 2 of the problem to you.\r
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