document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183249>Question 1183249</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A telephone call occurs at random in the interval (0, t). Let T be its time of<BR>\n" );
document.write( "occurrence. Determine, where 0 <= t0 <= t1 <= t<BR>\n" );
document.write( "(a) P(t0 <= T <= t1)<BR>\n" );
document.write( "(b) P(t0 <= T <= t1 | T >= t0)<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 #813481 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=813481\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (a)\r<BR>\n" );
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document.write( "I'm assuming we're dealing with a uniform distribution.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(t_0 \le T \le t_1) = \frac{t_1 - t_0}{t - 0}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(t_0 \le T \le t_1) = \frac{t_1 - t_0}{t}\">\r<BR>\n" );
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document.write( "There's not much more I can say since we don't know the values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B0%5D ALIGN=MIDDLE  ALT=\"t%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D ALIGN=MIDDLE  ALT=\"t%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large A = \frac{t_1 - t_0}{t}\"> which represents the probability T is between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B0%5D ALIGN=MIDDLE  ALT=\"t%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D ALIGN=MIDDLE  ALT=\"t%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We found this back in part (a)\r<BR>\n" );
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document.write( "Then we can say that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(T \ge t_0) = 1 - P(T \le t_0)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(T \ge t_0) = 1 - \frac{t_0}{t}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(T \ge t_0) = \frac{t}{t} - \frac{t_0}{t}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(T \ge t_0) = \frac{t-t_0}{t}\">\r<BR>\n" );
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document.write( "We'll assign this to the variable B. \r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(t_0 \le T \le t_1 \ \text{ given } \ T \ge t_0) = \frac{A}{B}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(t_0 \le T \le t_1 \ \text{ given } \ T \ge t_0) = A \div B\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(t_0 \le T \le t_1 \ \text{ given } \ T \ge t_0) = \frac{t_1 - t_0}{t} \div \frac{t-t_0}{t}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(t_0 \le T \le t_1 \ \text{ given } \ T \ge t_0) = \frac{t_1 - t_0}{t} \times \frac{t}{t-t_0}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(t_0 \le T \le t_1 \ \text{ given } \ T \ge t_0) = \frac{(t_1 - t_0)*t}{t*(t-t_0)}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(t_0 \le T \le t_1 \ \text{ given } \ T \ge t_0) = \frac{t_1 - t_0}{t-t_0}\">\r<BR>\n" );
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document.write( "I'm using the idea of conditional probability<BR>\n" );
document.write( "P(A given B) = P(A and B)/P(B)<BR>\n" );
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