document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187262>Question 1187262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the following probability mass function, 𝑓(𝑥) = 𝑃(𝑋 = 𝑥) = 𝑐(2𝑥 − 1) for x=1,2,3<BR>\n" );
document.write( "determine which of the statements below are true.<BR>\n" );
document.write( "I. The value of c is<BR>\n" );
document.write( "1<BR>\n" );
document.write( "3<BR>\n" );
document.write( ".<BR>\n" );
document.write( "II. The Expected value of the distribution is 2.44 (to 2 decimal places).<BR>\n" );
document.write( "III.<BR>\n" );
document.write( "P X( 1) 0.67  <BR>\n" );
document.write( "(to 2 decimal places).<BR>\n" );
document.write( "A. Only statements I and III are true.<BR>\n" );
document.write( "B. Only statement II is true.<BR>\n" );
document.write( "C. Only statements II and III are true.<BR>\n" );
document.write( "D. Only statement III is true. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818254 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818254\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I.<BR>\n" );
document.write( "P(1) = c(2-1) = c<BR>\n" );
document.write( "P(2) = c(4-1) = 3c<BR>\n" );
document.write( "P(3) = c(6-1) = 5c<br><BR>\n" );
document.write( "P(1)+P(2)+P(3) = c+3c+5c = 1; 9c=1; c=1/9<br><BR>\n" );
document.write( "I. is FALSE<br><BR>\n" );
document.write( "II.<BR>\n" );
document.write( "The expected value is<BR>\n" );
document.write( "(1/9)(1)+(3/9)(2)+(5/9)(3) = 22/9 = 2.44 (rounded)<br><BR>\n" );
document.write( "II. is TRUE<br><BR>\n" );
document.write( "III.<BR>\n" );
document.write( "I don't know what this part says....<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );