{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "#\n# L\366sungsvorsc hl\344ge zu Blatt 7\n#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "# \n# Aufgabe 1\n#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "M := r -> ((1/n)*sum(x[ i]^r,i=1..n))^(1/r);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "M(1) ;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "M(-1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "M(2);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 5 "M(3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "# lim M(r) f\374r r -> 0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "# n:=5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 " limit(M(r),r=0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "n:=3;" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "x[1]:=3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "x[2]:=5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "x[3]:=9;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "limit(M(r),r=0);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "%-3*5^(1/3);\nsimplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "#\n# Aufgabe 2\n#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "# Standardisierte Normalverteilung\nf := x -> exp(-x^ 2/2)/sqrt(2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(f( x),x=-3..3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "g := y -> 2 *int(f(x)*f(2*y-x),x=-infinity..infinity);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 5 "g(y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 " # Normalverteilung N(0,sigma^2)\nh := y -> exp(-y^2/(2*sigma^2))/(sigm a*sqrt(2*Pi));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "sigma := \+ sqrt(1/2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "h(y);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "# Cauchy-Verteilung" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 25 "f := x -> 1/(Pi*(1+x^2));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(f(x),x=-3..3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "g := y -> 2*int(f(x)*f(2*y-x),x=-infinity..in finity) assuming y :: real;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "g(y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalc(%);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "16 0 0" 23 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }