document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1027798>Question 1027798</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Q1 <BR>\n" );
document.write( "Suppose that the random variable X has the following cumulative distribution function:<BR>\n" );
document.write( "x	-1	1	3	5<BR>\n" );
document.write( "F(x)	1/4	1/2	3/4	1\r<BR>\n" );
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document.write( "	Find the probability distribution of this random variable.<BR>\n" );
document.write( "	Find p(x<3),p(x &#8805;1 )    <BR>\n" );
document.write( "	Find the mean of the random variable X.<BR>\n" );
document.write( "	Find the standard deviation of the random variable X.\r<BR>\n" );
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document.write( "Q2 \r<BR>\n" );
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document.write( "The cumulative distribution function of the random variable X is given by: \r<BR>\n" );
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document.write( "F(x)={0(1- 9/x^2 )   for3<x otherwise\r<BR>\n" );
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document.write( "	Find the probability density function for the random variable X.<BR>\n" );
document.write( "	compute p(X&#8804; 5) and p( 8< X )<BR>\n" );
document.write( "	Find the expected value for the random variable X. \r<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 #644388 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=644388\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Q1 <BR>\n" );
document.write( "Suppose that the random variable X has the following cumulative distribution function:<BR>\n" );
document.write( "x	-1	1	3	5<BR>\n" );
document.write( "F(x)	1/4	1/2	3/4	1 <BR>\n" );
document.write( "Find the probability distribution of this random variable.<BR>\n" );
document.write( "Find p(x<3),p(x &#8805;1 ) <BR>\n" );
document.write( "Find the mean of the random variable X.<BR>\n" );
document.write( "Find the standard deviation of the random variable X. \r<BR>\n" );
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document.write( "The pdf should be as follows:<BR>\n" );
document.write( "x	-1	1	3	5<BR>\n" );
document.write( "p(x)	1/4	1/4	1/4	1/4 <BR>\n" );
document.write( "Hence it is discrete uniformly distributed.<BR>\n" );
document.write( "p(x<3) = p(-1) + p(1) = 1/2, as can be directly read off from the table for F(x).<BR>\n" );
document.write( "p(x &#8805;1) = 1 - 1/4 = 3/4, as can be read off again from the table for F(x).<BR>\n" );
document.write( "Mean is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28X%29+=+%28-1%2B1%2B3%2B5%29%2A%281%2F4%29+=+2 ALIGN=MIDDLE  ALT=\"E%28X%29+=+%28-1%2B1%2B3%2B5%29%2A%281%2F4%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Variance is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Var%28X%29+=+E%28X%5E2%29+-+%28E%28X%29%29%5E2+=+%28%28-1%29%5E2%2B1%5E2%2B3%5E2%2B5%5E2%29%2A%281%2F4%29+-+2%5E2+=+36%2F4+-+4+=+9-4+=+5 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SD%28X%29+=+sqrt%285%29+=+2.236 ALIGN=MIDDLE  ALT=\"SD%28X%29+=+sqrt%285%29+=+2.236\"   DISABLED_style= \"max-width:90%; height:auto;\" > approximately<BR>\n" );
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