document.write( "Question 1197348: Suppose that a box contains 7 cameras and that 5 of them are defective. A sample of 2 cameras is selected at random, with replacement. Define the random variable
\n" ); document.write( "X as the number of defective cameras in the sample.\r
\n" ); document.write( "\n" ); document.write( "Write the probability distribution for X.\r
\n" ); document.write( "\n" ); document.write( "(Here there is a table on the left side it says 'k' and on the right side it says 'P(X=k)'.) There are three values on each side: on the left side there is '0,1,2' and on the right side there are 3 blank spots. Please find P(x=k).\r
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\n" ); document.write( "\n" ); document.write( "What is the expected value of X? \r
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Algebra.Com's Answer #830575 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Suppose that a box contains 7 cameras and that 5 of them are defective.
\n" ); document.write( "A sample of 2 cameras is selected at random, with replacement. Define the random variable
\n" ); document.write( "X as the number of defective cameras in the sample.
\n" ); document.write( "(a) Write the probability distribution for X.
\n" ); document.write( "(Here there is a table on the left side it says 'k' and on the right side it says 'P(X=k)'.)
\n" ); document.write( "There are three values on each side: on the left side there is '0,1,2'
\n" ); document.write( "and on the right side there are 3 blank spots. Please find P(x=k).\r
\n" ); document.write( "\n" ); document.write( "(b) What is the expected value of X?
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\n" ); document.write( "\n" ); document.write( "I interpret the problem as if in the experiment the cameras are taken from the set of 7 cameras
\n" ); document.write( "one after another with replacement, sequentially.\r
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\n" ); document.write( "\n" ); document.write( "It is a unique way to take the cameras \" with replacement \".\r
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\n" ); document.write( "\n" ); document.write( " Part (a)\r
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document.write( "P(X=0) means the probability of having 0 (zero) defective cameras among 2 selected from 7.\r\n" );
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document.write( "    P(X=0) =  = .    <<<---===  every time we select from 7-5 = 2 good cameras\r\n" );
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document.write( "P(X=1) means the probability of having 1 (one) defective camera among 2 selected from 7.\r\n" );
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document.write( "    P(X=1) = P(1st is defective, 2nd is good) + P(1st is good,2nd is defective) = \r\n" );
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document.write( "           =  =  = .\r\n" );
document.write( "    \r\n" );
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document.write( "P(X=2) means the probability of having 2 (two) defective cameras among 2 selected from 7.\r\n" );
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document.write( "    P(X=2) = P(1st is defective, 2nd is defective) = \r\n" );
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document.write( "           =  = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Part (a) is complete.\r
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document.write( "Math expectation = 0*P(X=0) + 1*P(X=1) + 2*P(X=2) = 0 +  +  =  =  = 1 = 1 = 1.3.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Part (b) is complete.\r
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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