document.write( "Question 415070: A bag contains 22 cubes, of which 11 are red. Three cubes are drawn without replacement. Let X be the number of red cubes drawn. Find the variance of X. \n" ); document.write( "

Algebra.Com's Answer #291032 by robertb(5830) $\"\"$ $\"About$

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The pmf is $\"p%28x%29+=+3Cx%2A%281%2F2%29%5E%283-x%29%2A%281%2F2%29%5Ex+=+3Cx%2F8\"$ . Hence\r
\n" ); document.write( "\n" ); document.write( "X ----> 0 1 2 3
\n" ); document.write( "p(x)--> 0.125 0.375 0.375 0.125\r
\n" ); document.write( "\n" ); document.write( "==> $\"mu+=+0.375+%2B+2%2A0.375+%2B+3%2A0.125+=+1.5\"$
\n" ); document.write( "==> $\"Var%28X%29+=+E%28X%5E2%29+-+%28E%28X%29%29%5E2+=+3+-+1.5%5E2+=+0.75\"$ .\r
\n" ); document.write( "\n" ); document.write( "A shorter solution is as follows: The mean $\"mu\"$ for a binomial experiment is n*p = 3*0.5 = 1.5, while the variance is n*p*q = 3*0.5*0.5 = 0.75. (Here, n = 3, and p = q = 0.5.) \n" ); document.write( "

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