document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200583>Question 1200583</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A workplace injury policy has a premium (policy cost) of $7. The probability of a claim is<BR>\n" );
document.write( "0.43, in which case the amount of the claim has density 1.2/(𝑥^2.2), when 𝑥 ≥ 1. Find the expected<BR>\n" );
document.write( "value of the net revenue to the company. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848086 by </B><A HREF=/tutors/aboutme.mpl?userid=GingerAle><B>GingerAle(43)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=GingerAle><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=848086\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Define Net Revenue**\r<BR>\n" );
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document.write( "* **Net Revenue = Premium Revenue - Expected Claim Cost**\r<BR>\n" );
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document.write( "**2. Calculate Premium Revenue**\r<BR>\n" );
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document.write( "* Premium Revenue = Premium per policy * Probability of no claim + Premium per policy * Probability of claim<BR>\n" );
document.write( "* Premium Revenue = $7 * (1 - 0.43) + $7 * 0.43 = $7 \r<BR>\n" );
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document.write( "**3. Calculate Expected Claim Cost**\r<BR>\n" );
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document.write( "* **Expected Claim Cost = Probability of claim * Expected claim amount**\r<BR>\n" );
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document.write( "* **Find Expected Claim Amount:**\r<BR>\n" );
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document.write( "   * Expected Claim Amount = ∫(x * f(x)) dx <BR>\n" );
document.write( "      where f(x) is the probability density function of the claim amount <BR>\n" );
document.write( "      and the integral is taken over the range of possible claim amounts (x ≥ 1)\r<BR>\n" );
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document.write( "   * Expected Claim Amount = ∫(x * (1.2/x^2.2)) dx from 1 to infinity<BR>\n" );
document.write( "   * Expected Claim Amount = 1.2 ∫(x^(-1.2)) dx from 1 to infinity\r<BR>\n" );
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document.write( "   * To solve this improper integral, we need to find the limit as the upper bound approaches infinity:\r<BR>\n" );
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document.write( "      * Expected Claim Amount = 1.2 * lim (b→∞) [(-1/0.2) * x^(-0.2)] from 1 to b<BR>\n" );
document.write( "      * Expected Claim Amount = -6 * lim (b→∞) [b^(-0.2) - 1^(-0.2)]<BR>\n" );
document.write( "      * Expected Claim Amount = -6 * (0 - 1) = 6\r<BR>\n" );
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document.write( "* **Expected Claim Cost = 0.43 * 6 = 2.58**\r<BR>\n" );
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document.write( "**4. Calculate Net Revenue**\r<BR>\n" );
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document.write( "* Net Revenue = $7 - $2.58 = $4.42\r<BR>\n" );
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document.write( "**Therefore, the expected value of the net revenue to the company is $4.42.**<BR>\n" );
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