document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=752187>Question 752187</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to find E(x^2) in Probability distribution<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #457624 by </B><A HREF=/tutors/aboutme.mpl?userid=reviewermath><B>reviewermath(1029)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reviewermath><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=reviewermath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=457624\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Q: How to find E(X^2) in Probability distribution<BR>\n" );
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document.write( "A: If you know the mean and variance of the random variable X, then use<BR>\n" );
document.write( "the equation Var(X) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28X%5E2%29+-+%28E%28X%29%29%5E2 ALIGN=MIDDLE  ALT=\"E%28X%5E2%29+-+%28E%28X%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for <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;\" >.<BR>\n" );
document.write( "If you don't know the mean and variance, then use the following formulas:<BR>\n" );
document.write( "1. If X is a continuous random variable then <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;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28+%28x%5E2%29f%28x%29%2C+dx%2C+-infinity%2C+infinity+%29 ALIGN=MIDDLE  ALT=\"int%28+%28x%5E2%29f%28x%29%2C+dx%2C+-infinity%2C+infinity+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where f(x) represents the probability distribution function of X.\r<BR>\n" );
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document.write( "2. If X is a discrete random variable then <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;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28%28x%5E2%29p%28x%29%29 ALIGN=MIDDLE  ALT=\"sum%28%28x%5E2%29p%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, for all values of x, where p(x) represents the probability mass function of X. </SPAN>\n" );
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