document.write( "Question 1189203: Given that E(X) = 2.5, find a and b.\r
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\n" ); document.write( "P(X=x) 0.3 a b 0.2 \n" ); document.write( "

Algebra.Com's Answer #820501 by ikleyn(52852) $\"\"$ $\"About$

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\n" ); document.write( "Given that E(X) = 2.5, find a and b.\r
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document.write( "X =      1  2  3  4\r\n" );
document.write( "P(X=x)  0.3 a  b  0.2\r\n" );
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document.write( "From  P(1) + P(2) + P(3) + P(4) = 1,  you have one equation\r\n" );
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document.write( "    0.3 + a + b + 0.2 = 1,\r\n" );
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document.write( "or\r\n" );
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document.write( "    a + b = 0.5.       (1)\r\n" );
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document.write( "From E(X)=2.5, you have another equation\r\n" );
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document.write( "    1*0.3 + 2a + 3b + 4*0.2 = 2.5,\r\n" );
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document.write( "or\r\n" );
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document.write( "    2a + 3b = 1.4.     (2)\r\n" );
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document.write( "Thus you have a system of two equations\r\n" );
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document.write( "     a +  b = 0.5      (1)\r\n" );
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document.write( "    2a + 3b = 1.4      (2)\r\n" );
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document.write( "To solve, multiply equation (1) by 2 (both sides); then subtract from equation (2). You will get then\r\n" );
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document.write( "         3b - 2b = 1.4 - 2*0.5\r\n" );
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document.write( "            b    = 0.4\r\n" );
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document.write( "Then from equation (1)\r\n" );
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document.write( "             a  = 0.5 - 0.4 = 0.1.\r\n" );
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document.write( "ANSWER.  a= 0.1;  b= 0.4.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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