document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198127>Question 1198127</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a. The following table gives the joint probability distribution of the random<BR>\n" );
document.write( "variables X and Y , where X is the first  -  year rate of return expected<BR>\n" );
document.write( "from investment A while Y is the first  -  year rate of return expected from<BR>\n" );
document.write( "investment B.<BR>\n" );
document.write( "Table 5: Rates of Return on Two Investments\r<BR>\n" );
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document.write( "Y(%)				X(%)<BR>\n" );
document.write( "	-10	0	20	30<BR>\n" );
document.write( "20	0.27	0.08	0.16	0<BR>\n" );
document.write( "50	0	0.04	0.1	0.35\r<BR>\n" );
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document.write( "i. Calculate the expected rate of return from investment B.<BR>\n" );
document.write( "ii. Find the conditional expectation of Y , given X = 20.<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 #848345 by </B><A HREF=/tutors/aboutme.mpl?userid=onyulee><B>onyulee(41)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=onyulee><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=848345\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **i. Calculate the expected rate of return from investment B**\r<BR>\n" );
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document.write( "* To calculate the expected rate of return from investment B, we'll sum the products of each possible return of B (Y) and its corresponding probability.\r<BR>\n" );
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document.write( "* **Expected Return of B (E[Y]) =** <BR>\n" );
document.write( "    * (20% * 0.27) + (20% * 0.08) + (20% * 0.16) + (50% * 0) + (50% * 0.04) + (50% * 0.1) + (50% * 0.35) <BR>\n" );
document.write( "    * = 5.4 + 1.6 + 3.2 + 0 + 2 + 17.5 <BR>\n" );
document.write( "    * = **34.7%**\r<BR>\n" );
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document.write( "**ii. Find the conditional expectation of Y, given X = 20**\r<BR>\n" );
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document.write( "* We need to find the expected return of investment B (Y) when investment A (X) has a return of 20%.\r<BR>\n" );
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document.write( "* **Conditional Probability Table (X = 20):**\r<BR>\n" );
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document.write( "| Y(%) | Probability (given X = 20) |<BR>\n" );
document.write( "|---|---|<BR>\n" );
document.write( "| 20 | 0.16 / (0.16 + 0.1) = 0.6154 |<BR>\n" );
document.write( "| 50 | 0.1 / (0.16 + 0.1) = 0.3846 |\r<BR>\n" );
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document.write( "* **Conditional Expectation of Y given X = 20 (E[Y|X=20]) =** <BR>\n" );
document.write( "    * (20% * 0.6154) + (50% * 0.3846) <BR>\n" );
document.write( "    * = 12.308 + 19.231 <BR>\n" );
document.write( "    * = **31.539%**\r<BR>\n" );
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document.write( "**In summary:**\r<BR>\n" );
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document.write( "* The expected rate of return from investment B is **34.7%**.<BR>\n" );
document.write( "* The conditional expectation of Y (the return on investment B) given that X (the return on investment A) is 20% is **31.539%**.<BR>\n" );
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