document.write( "Question 1203804: A discrete random variable X has a pdf of the form f(x) = c(8 - x) for x = 0, 1, 2, 3, 4, 5, and zero otherwise.
\n" ); document.write( "(a) Find the constant c.
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\n" ); document.write( "(c) Find P[X > 2]
\n" ); document.write( "(d) Find E(X). \n" ); document.write( "

Algebra.Com's Answer #839938 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
A discrete random variable X has a pdf (of the form f(x) = c(8 - x) for
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document.write( "n              f(n)\r\n" );
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document.write( "0  c(8 - 0) = 8c         = 8/33\r\n" );
document.write( "1  c(8 - 1) = 7c         = 7/33\r\n" );
document.write( "2  c(8 - 2) = 6c         = 6/33 \r\n" );
document.write( "3  c(8 - 3) = 5c         = 5/33\r\n" );
document.write( "4  c(8 - 4) = 4c         = 4/33\r\n" );
document.write( "5  c(8 - 5) = 3c         = 3/33\r\n" );
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document.write( "      total = 33c = 1       \r\n" );
document.write( "                c = 1/33

\n" ); document.write( "(b) Find the CDF, F(x).

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document.write( "n                                  F(n)\r\n" );
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document.write( "0  F(0) = f(0) = 8/33\r\n" );
document.write( "1  F(1) = F(0)+f(1) =  8/33+7/33 = 15/33\r\n" );
document.write( "2  F(2) = F(1)+f(2) = 15/33+6/33 = 21/33 \r\n" );
document.write( "3  F(3) = F(2)+f(3) = 21/33+5/33 = 26/33\r\n" );
document.write( "4  F(4) = F(3)+f(4) = 26/33+4/33 = 30/33\r\n" );
document.write( "5  F(5) = F(4)+f(5) = 30/33+3/33\r\n" );
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\n" ); document.write( "(c) Find P[X > 2]

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document.write( "P[X > 2] = P[X = 3] + P[X = 4] + P[X = 5] = 5/33 + 4/33 + 3/33 = 12/33 = 4/11\r\n" );
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document.write( "or you could do it this way if there were very many fewer this way:\r\n" );
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document.write( "P[X > 2] = 1 - P[x < F(2) = 1 - 21/33 = 33/33 - 21/33 = 12/33 = 4/11

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document.write( "Edwin

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