document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=855493>Question 855493</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I cannot figure out this problem:<BR>\n" );
document.write( "The useful life of an electrical component is exponentially distributed with a mean of 4000 hours.<BR>\n" );
document.write( "a. What is the probability the circuit will last more than 4500 hours?<BR>\n" );
document.write( "b. What is probability the circuit will last between 4000 and 4750 hours?<BR>\n" );
document.write( "c. What is probability the circuit will fail within the first 3250 hours?<BR>\n" );
document.write( "I cannot figure out what the value of e is, or the value of lambda symbol.<BR>\n" );
document.write( "Thanks for your help.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #515402 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=515402\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The expected value (E) is the mean of an exponential distribution<BR>\n" );
document.write( "E[X] = 1 / lamda = 4000<BR>\n" );
document.write( "lamda = 1 / 4000<BR>\n" );
document.write( "f(x, lamda) = lamda * e^(-lamda*x)<BR>\n" );
document.write( "note that e is equal to 2.71828<BR>\n" );
document.write( "a) P(X>4500) = e^(-4500*lamda) = 2.71828^(-4500*1/4000)<BR>\n" );
document.write( " P(X>4500) = 0.32<BR>\n" );
document.write( "b)P(4000 < X < 4750) = P(X>4000) - P(X>4750)<BR>\n" );
document.write( "P(4000 < X < 4750) =  e^(-4000*lamda) - e^(-4750*lamda)<BR>\n" );
document.write( "P(4000 < X < 4750) =   .37 - .30 = 0.07<BR>\n" );
document.write( "c)P(X<3250) = 1 - P(X>3250)<BR>\n" );
document.write( "P(X<3250) = 1 - e^(-3250*lamda)= 1 - 0.44 = 0.56\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );