document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=444189>Question 444189</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve these problems:\r<BR>\n" );
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document.write( "Given the probability distribution of a random variable<BR>\n" );
document.write( "outcome: -2, 4, 10<BR>\n" );
document.write( "probability: 0.80, 0.15, 0.05\r<BR>\n" );
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document.write( "3. Compute the expected value (one digit after decimal point).<BR>\n" );
document.write( "4. Compute the variance (two digits after decimal point). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #306266 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=306266\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The expected value of a discrete random variable x is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28x%29+=+sum%28+x%5Bi%5Dp%5Bi%5D%2C+i%29 ALIGN=MIDDLE  ALT=\"E%28x%29+=+sum%28+x%5Bi%5Dp%5Bi%5D%2C+i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bi%5D ALIGN=MIDDLE  ALT=\"x%5Bi%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the outcomes and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5Bi%5D ALIGN=MIDDLE  ALT=\"p%5Bi%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > are their probabilities<BR>\n" );
document.write( "Using the values x = -2, 4, 10; p = 0.8, 0.15, 0.05, we get<BR>\n" );
document.write( "E(x) = -2*0.8 + 4*0.15 + 10*0.05 = -0.5<BR>\n" );
document.write( "The variance of a discrete random variable x is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma%5E2+=+sum%28%28x%5Bi%5D+-+E%28x%29%29%5E2%2Ap%5Bi%5D%2Ci%29 ALIGN=MIDDLE  ALT=\"sigma%5E2+=+sum%28%28x%5Bi%5D+-+E%28x%29%29%5E2%2Ap%5Bi%5D%2Ci%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So we have <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma%5E2 ALIGN=MIDDLE  ALT=\"sigma%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (-2 - -0.5)^2 + (4 - -0.5)^2 + (10 - -0.5)^2 = 10.35 </SPAN>\n" );
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