document.write( "Question 1149314: Five-digit codes are selected at random from the set {0, 1, 2, ..., 9} with replacement. If the random variable X denotes the number of zeros in randomly chosen codes, then what are the space and the probability density function of X? \n" ); document.write( "

Algebra.Com's Answer #770674 by ikleyn(52810) $\"\"$ $\"About$

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document.write( "The first sentence means that repetitions are allowed in the code's digits.\r\n" );
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document.write( "The possible values for the random variable X are {0, 1, 2, 3, 4, 5}.\r\n" );
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document.write( "X= 0  means that there is NO zero among five digits of the code.\r\n" );
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document.write( "      The probability do not have zero in any one fixed/selected of 5 positions is  ;\r\n" );
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document.write( "      The provability do not have zero in ALL        5 positions, is, therefore,  .\r\n" );
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document.write( "X= 1  means that there is exactly one 0 among five digits of the code.\r\n" );
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document.write( "      The probability for it is   = .\r\n" );
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document.write( "X= 2  means that there is exactly two 0 among five digits of the code.\r\n" );
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document.write( "      The probability for it is  .\r\n" );
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document.write( "The pattern is just clear.  The probability for X = k,  where  k= 0, 1, 2, 3, 4, 5,  is\r\n" );
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document.write( "            .   \r\n" );
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\n" ); document.write( "\n" ); document.write( "CHECK. You may check that the sum of these 6 partial probabilities is 1.\r
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document.write( "    Indeed, this sum is equal to   =  = 1.\r\n" );
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