document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1109861>Question 1109861</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider a loaded die, in 10 independent throws the probability that an even number turns up 5 times is twice the probability that even number turns up 4 times. Prepare the probability distribution of the even numbers and compute the mean and variance. Verify your results as. <BR>\n" );
document.write( "1) &#956; = E(x) = np 2) Var(x) = &#963;^2 = npq <BR>\n" );
document.write( "Where p = prob. of even number q = 1-p </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #724830 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=724830\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider a loaded die, in 10 independent thr<BR>\n" );
document.write( "ows the probability that an even number turns up 5 times is twice the probability that even number turns up 4 times. Prepare the probability distribution of the even numbers and compute the mean and variance. Verify your results as. <BR>\n" );
document.write( "1) mean = E(x) = np <BR>\n" );
document.write( "2) Var(x) = sigma^2 = npq <BR>\n" );
document.write( "Where p = prob. of even number q = 1-p<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "P(x = 5) = 10C5p^5q^5<BR>\n" );
document.write( "P(x = 4) = 10C4p^4q^6<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "10C5p^5q^5 = 2[10C4p^4q^6]<BR>\n" );
document.write( "p/q = [2*10C4]/10C5 = 5/3<BR>\n" );
document.write( "----<BR>\n" );
document.write( "p = (5/3)q<BR>\n" );
document.write( "p + q = 1<BR>\n" );
document.write( "p + (3/5)p = 1<BR>\n" );
document.write( "8/5 p = 1<BR>\n" );
document.write( "p = 5/8<BR>\n" );
document.write( "1) mean = n*p = 10(5/8) = 50/8 = 6.25<BR>\n" );
document.write( "2) Var = npq = 6.25(3/8) = 2.344<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "----------\r<BR>\n" );
document.write( "\n" );
document.write( "-----\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );