document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=381445>Question 381445</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The probability distribution of a discrete random variable X is shown below \r<BR>\n" );
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document.write( "x	0	1	2	3<BR>\n" );
document.write( "p(x)	0.25	0.40	0.20	0.15\r<BR>\n" );
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document.write( "1) Find the expected value of X and the standard deviation of X <BR>\n" );
document.write( "2) Suppose another random variable, Y = -3X-2. Then find the expected value of Y and the standard deviation of Y <BR>\n" );
document.write( "-3X-2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #270560 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=270560\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+0%2A0.25+%2B+1%2A0.40+%2B+2%2A0.20+%2B+3%2A0.15+=+0.40+%2B+0.40+%2B+0.45+=+1.25 ALIGN=MIDDLE  ALT=\"mu+=+0%2A0.25+%2B+1%2A0.40+%2B+2%2A0.20+%2B+3%2A0.15+=+0.40+%2B+0.40+%2B+0.45+=+1.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma+=+sqrt%28%280-1.25%29%5E2%2A0.25+%2B+%281-1.25%29%5E2%2A0.40+%2B+%282-1.25%29%5E2%2A0.20+%2B+%283-1.25%29%5E2%2A0.15%29+=+sqrt%280.390625+%2B+0.025%2B0.1125%2B0.459375%29+=+sqrt%280.9875%29+=+0.99373 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "2) E(-3X-2) = -3E(X) - 2 = -3*1.25-2 = -5.75.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Var%28-3X+-+2%29+=+9Var%28X%29 ALIGN=MIDDLE  ALT=\"Var%28-3X+-+2%29+=+9Var%28X%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28Var%28-3X+-+2%29%29+=+3sqrt%28Var%28X%29%29+=+3sigma ALIGN=MIDDLE  ALT=\"sqrt%28Var%28-3X+-+2%29%29+=+3sqrt%28Var%28X%29%29+=+3sigma\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Hence standard deviation of Y = -3X-2 is 3*0.99373 = 2.98119. </SPAN>\n" );
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