document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1022893>Question 1022893</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A chemical supply company ships a certain solvent in 10&#8722;gallon drums. Let X represent the number of drums ordered by a randomly chosen customer. Assume X has the following probability mass function:<BR>\n" );
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document.write( "x	    1	    2   	3	  4     	5<BR>\n" );
document.write( "p(x)   0.36  0.19    0.17   0.06	0.22\r<BR>\n" );
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document.write( "Find the variance of the number of drums ordered.<BR>\n" );
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document.write( "The variance of number of drums ordered = </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #638458 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=638458\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We make use of the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Var%28X%29+=+E%28X%5E2%29+-+%28E%28X%29%29%5E2 ALIGN=MIDDLE  ALT=\"Var%28X%29+=+E%28X%5E2%29+-+%28E%28X%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "To find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28X%5E2%29 ALIGN=MIDDLE  ALT=\"E%28X%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we find pmf of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2 ALIGN=MIDDLE  ALT=\"X%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2 ALIGN=MIDDLE  ALT=\"X%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >        1     4      9      16      25<BR>\n" );
document.write( "p(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2%29 ALIGN=MIDDLE  ALT=\"X%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)  0.36   0.19  0.17    0.06    0.22\r<BR>\n" );
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document.write( "which is identical to the pmf of X.<BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28X%5E2%29+=+1%2A0.36%2B+4%2A0.19+%2B+9%2A0.17+%2B+16%2A0.06+%2B+25%2A0.22+=+9.11 ALIGN=MIDDLE  ALT=\"E%28X%5E2%29+=+1%2A0.36%2B+4%2A0.19+%2B+9%2A0.17+%2B+16%2A0.06+%2B+25%2A0.22+=+9.11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now E(X) = 0.36 + 2*0.19 + 3*0.17 + 4*0.06 + 5*0.22 = 2.59\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Var%28X%29+=+9.11+-+2.59%5E2+=+2.4019 ALIGN=MIDDLE  ALT=\"Var%28X%29+=+9.11+-+2.59%5E2+=+2.4019\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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