{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q1" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "lambda:=5.36:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 70 " F:=1-exp(-lambda*Pi*x^2): f:=diff(F,x): m u:=int(x*f,x=0..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG$ \"+k5nf@!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "sqrt(int((x- mu)^2*f,x=0..infinity));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+r,\"*G 6!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "L:=evalf(Pi*3*lambda): add( L^i/i!*exp(-L),i=0..49);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+3MdAX! #5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "35*lambda/2; sqrt(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"++++!Q*!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+5+/&o*!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q 2" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "res tart: lambda:=12.8: P:=(0.4/(1-0.6*z))^3: PGF:=exp(lambda*23/60*(P- 1)):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "mu:=eval(diff(PGF,z),z=1); e val(diff(PGF,z,z),z=1)+mu-mu^2: sqrt(%); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG$\"++++3A!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# $\"+A;AV7!\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "prob:=mtaylor(PGF, z,11): 1-eval(prob,z=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+DYv7# )!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "L:=23/60*lambda*eval(P,z=0): exp(-L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+za*\\I(!#5" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q3" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "restart: lambda:=17.3/60: g:=piecew ise(s>5,50/s^3,0): G:=int(g,s):" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "t:=38: pt:=int(1-G,s=0..t)/t: Lx:=lambda*pt*t: Ly:=l ambda*(1-pt)*t:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "add(Lx^i /i!*exp(-Lx),i=0..4)*(1-add(Ly^i/i!*exp(-Ly),i=0..7));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+AdBP]!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "Linf:=lambda*int(1-G,s=0..infinity): exp(-Linf);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+\\ez%f&!#6" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c )" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "1/l ambda; # in minutes" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+$43#oM!\"* " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q4" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "restart: lambda:=20-(t-13)^ 2/3: " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "L:=int(lambda,t=11.+45/60.. 13+25/60): 1-add(L^i/i!*exp(-L),i=0..39);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+m0*QM\"!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b )" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "L1: =int(lambda,t=9..9+17/60.): L2:=int(lambda,t=9..9+32/60.):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "(1+L1+L1^2/2)*exp(-L1)-(1+L2+L2^2/2 )*exp(-L2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+yU90>!#5" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "L:=int(lambda,t=9..u): F:=1-(1+L+L ^2/2)*exp(-L): f:=simplify(diff(F,u)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "res:=evalf(int(u*f,u=9..17));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$resG$\"+)3%))*>*!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q5" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "restart: P:=2^2.5/(3-exp(4*z-4))^2.5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "mu:=eval(diff(P,z),z=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG$\"+++++]!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "eval(diff(P,z,z),z=1)+mu-mu^2: simplify(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#N\"\"!" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 28 "1-eval(mtaylor(P,z,10),z=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+\"[,`(=!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "1-eval(mtaylor(P^7,z,10),z=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#$\"+#*pPI(*!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "42 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }