diff --git a/ea/Ub4/A3a.m b/ea/Ub4/A3a.m index c6c14b7..3ec8c6a 100644 --- a/ea/Ub4/A3a.m +++ b/ea/Ub4/A3a.m @@ -9,7 +9,7 @@ mh1= m1*fh1/fp*(1-pc*d1/(l-1)-o1*pm) m2=1 -fh2=4 +fh2=2 o2=3 d2=4 diff --git a/ea/Ub4/ea4.pdf b/ea/Ub4/ea4.pdf index b43d055..051080c 100644 --- a/ea/Ub4/ea4.pdf +++ b/ea/Ub4/ea4.pdf Binary files differ diff --git a/ea/Ub4/ea4.tex b/ea/Ub4/ea4.tex index 4968a8e..51030cd 100644 --- a/ea/Ub4/ea4.tex +++ b/ea/Ub4/ea4.tex @@ -85,9 +85,12 @@ P(X=K)= b(k|p_i;|P|) = \binom{|P|}{k}\cdot p_i^k\cdot(1-p_i)^{n-k} $ \item $p_{i,neu}= m\cdot p_i$ - \item $\mu = |P|\cdot p_i\\ - \sigma^2 = |P| \cdot p_i \cdot (1-p_i) + \item $\mu = |P|\cdot p_i\\$ + Da jedes Individuum mit Wahrscheinlichkeit p Nachkomme von dem Individuum der Elterngeneration ist.\\ $ + \sigma^2 = n\cdot(E(X^2)-E^2(X)) = |P| \cdot p_i \cdot (1-p_i) + $ + \\ \item \begin{itemize} \item $p_1= 0.01\\ @@ -151,7 +154,7 @@ x00x&0,1,14,15&49.5\\ x01x&2,3,12,13&25.5\\ x10x&6,7,8,9&1.5\\ - x11x&4,5,10,11&0.5\\ + x11x&4,5,10,11&9.5\\ \end{tabular} \\ Beste Fitness: $x10x$ mit 1.5\\ \end{itemize} @@ -165,19 +168,21 @@ l=6\\$ \begin{itemize} \item $H_1\\ - mH_1(t)= 5\\ + m(H_1,t)= 5\\ f(H_1)= \dfrac{21}{5} = 4.2\\ o_1=2\\ \delta_1=1\\ \rightarrow - m(H_1,t+1) \geq 6.2222$ + m(H_1,t+1) \geq 6.2222$\\ + Die Anzahl der Exemplare des Schemas H1 vergrößert sich um mindestens 24.44\% \item $H_2\\ - mH_2(t)= 1\\ - f(H_2)= \dfrac{21}{5} = 4\\ + m(H_2,t)= 1\\ + f(H_2)= 2\\ o_2=3\\ \delta_2=4\\ \rightarrow - m(H_2,t+1) \geq 0.5185$ + m(H_2,t+1) \geq 0.2593$\\ + Die Anzahl der Exemplare des Schemas H2 verringert sich um höchstens 74.07\% \end{itemize} diff --git a/ea/Ub4/plotcode.rtf b/ea/Ub4/plotcode.rtf new file mode 100644 index 0000000..8b12329 --- /dev/null +++ b/ea/Ub4/plotcode.rtf @@ -0,0 +1,72 @@ +{\rtf1\ansi\ansicpg1252\cocoartf1344\cocoasubrtf720 +{\fonttbl\f0\fmodern\fcharset0 Courier;} +{\colortbl;\red255\green255\blue255;\red160\green32\blue240;} +\paperw11900\paperh16840\margl1440\margr1440\vieww10800\viewh8400\viewkind0 +\deftab720 +\pard\pardeftab720 + +\f0\fs20 \cf0 y = @(x) x^2 +\fs24 \ + +\fs20 +\fs24 \ + +\fs20 xv = [-32:31] +\fs24 \ + +\fs20 yv = arrayfun(y,xv) +\fs24 \ + +\fs20 +\fs24 \ + +\fs20 H3= [(-8:-1);(24:31)] +\fs24 \ + +\fs20 H3y= arrayfun(y,H3) +\fs24 \ + +\fs20 +\fs24 \ + +\fs20 H4=[-32,-31,-26,-25,-16,-15,-8,-7,0,1,8,9,16,17,24,25] +\fs24 \ + +\fs20 H4y= arrayfun(y,H4) +\fs24 \ + +\fs20 hold \cf2 all +\fs24 \cf0 \ +\pard\pardeftab720 + +\fs20 \cf2 +\fs24 \cf0 \ +\pard\pardeftab720 + +\fs20 \cf0 stem(H3,H3y,\cf2 '-.g*'\cf0 ); +\fs24 \ + +\fs20 stem(H4,H4y,\cf2 ':r*'\cf0 ); +\fs24 \ + +\fs20 plot(xv,yv,\cf2 'b*'\cf0 ); +\fs24 \ + +\fs20 +\fs24 \ + +\fs20 xlabel(\cf2 'x'\cf0 ); +\fs24 \ + +\fs20 ylabel(\cf2 'y'\cf0 ); +\fs24 \ + +\fs20 +\fs24 \ + +\fs20 hold \cf2 off +\fs24 \cf0 \ + +\fs20 legend(\cf2 'Loesungsraum H3'\cf0 ,\cf2 'Loesungsraum H4'\cf0 ,\cf2 'f(x)=x^2'\cf0 ) +\fs24 \ +} \ No newline at end of file diff --git a/mr/Ub4/A3.mn b/mr/Ub4/A3.mn index 75be61a..5fc0b23 100644 --- a/mr/Ub4/A3.mn +++ b/mr/Ub4/A3.mn Binary files differ diff --git a/mr/Ub4/mr4.pdf b/mr/Ub4/mr4.pdf index 928a2d6..aa072d1 100644 --- a/mr/Ub4/mr4.pdf +++ b/mr/Ub4/mr4.pdf Binary files differ diff --git a/mr/Ub4/mr4.tex b/mr/Ub4/mr4.tex index 2479b69..6608b98 100644 --- a/mr/Ub4/mr4.tex +++ b/mr/Ub4/mr4.tex @@ -117,52 +117,53 @@ \Aufgabe{}{8} \begin{enumerate}[(a)] \item $ ^bg= - ^b\mathbf{R}_w^{-1} \cdot \begin{pmatrix} + ^b\mathbf{R}_w \cdot \begin{pmatrix} 0 \\ 0\\ -g \end{pmatrix} $ \item $ - ^ba_m = b_g+^ba_l\\ + ^ba_m = ^bg+^ba_l\\ $ - if $ ba_l=0$ \\ + if $ ^ba_m=0$ \\ $ - ^ba_m = b_g + ^ba_l = -^bg $ \item \begin{align*} - ^ba_m &= b_g+^ba_l\\ &= ^b\mathbf{R}_w^{-1} \cdot \begin{pmatrix} + ^ba_m &= b_g+^ba_l\\ &= ^b\mathbf{R}_w \cdot \begin{pmatrix} 0 \\ 0\\ -g - \end{pmatrix} +^ba_l\\ + \end{pmatrix} \\ &= \begin{pmatrix} - sin(\theta)g+ ^ba_{l,x} \\-cos(\theta)*sin(\phi)g +^ba_{l,y} \\ -cos(\theta)*cos(\phi)g +^ba_{l,z} + sin(\theta)g \\-cos(\theta)*sin(\phi)g \\ -cos(\theta)*cos(\phi)g \end{pmatrix}\\ - ^ba_{m,x}&= sin(\theta)g+ ^ba_{l,x} \\ - \theta &= sin^{-1}(\frac{^ba_{m,x}-^ba_{l,x}}{g})=0\\ - ^ba_{m,y} &= -g\cdot sin(\phi)\cdot (\frac{\pi}{2}-\frac{^ba_{m,x}-^ba_{l,x}}{g})) + ^ba_{l,y}\\ - \phi&= sin^{-1}(\frac{^ba_{m,y}-^ba_{l,y}}{-\frac{ - \pi}{2}g+^ba_{m,x}-^ba_{l,x}}) =0 + ^ba_{m,x}&= sin(\theta)g \\ + \theta &= sin^{-1}(\frac{^ba_{m,x}}{g})\\ + ^ba_{m,y} &= -g\cdot sin(\phi)\cdot \sqrt{1-\left(\frac{^ba_x}{g}\right)^2} \\ + \phi&= \sin^{-1} \left(-\frac{^ba_y}{g*\sqrt{1-\left(\frac{^ba_x}{g}\right)^2}}\right) \end{align*} \end{enumerate} \Aufgabe{}{8} \begin{enumerate}[(a)] \item \begin{align*} - \frac{g*M}{RT_0} &:= K\\ - \ensuremath{[}K\ensuremath{]} &= \dfrac{1}{m}\\ - K&= 1.1854 *10^{-4} \dfrac{1}{m}\\ - p_0 &= 101325 Pa\\ - p(a)&= p_0 \cdot exp(-Ka)\\ - p(a)_{lin&}= p(\overline{a}) + p'(\overline{a})\cdot (\overline{a}-a)\\ - p'(\overline{a})& = -K\cdot p_0 \cdot exp(-K\overline{a})\\ - p(a)_{lin&}= p_0 \cdot exp(-K\overline{a}) -K\cdot p_0 \cdot exp(-K\overline{a})\cdot (a-\overline{a})\\ - &= p_0 \cdot exp(-K\overline{a})(1-K(a-\overline{a}) + \frac{g*M}{RT_0} &=: \beta\\ + \left[\beta\right] &= \dfrac{1}{m}\\ + \beta& \approx 1.1854 *10^{-4} \dfrac{1}{m}\\ + p_0 &= 101325 Pa\\ + p(a)&= p_0 \cdot exp(-\beta a)\\ + p(a)_{lin}&= p(\overline{a}) + p'(\overline{a})\cdot (\overline{a}-a)\\ + p'(\overline{a})& = -\beta\cdot p_0 \cdot exp(-\beta\overline{a})\\ + p(a)_{lin}&= p_0 \cdot exp(-\beta\overline{a}) -\beta\cdot p_0 \cdot exp(-\beta\overline{a})\cdot (a-\overline{a})\\ + &= p_0 \cdot exp(-\beta\overline{a})(1-\beta(a-\overline{a})) \end{align*} \item \begin{align*} \overline{a}_1&= 100m \\ +p(a)_{lin1} &= p_0 \cdot exp(-\beta100m)(1-\beta(a-100m))\\ p(a)_{lin1} &= 101317.937 - 11.86959596*a \\ \overline{a_2}&= 10000m\\ - p(a)_{lin2} &= 100666.9318 - 10.66847938*a\\ - TODO Nachrechnen\\ \end{align*} +p(a)_{lin1} &= p_0 \cdot exp(-\beta 10000m)(1-\beta(a-10000m))\\ + p(a)_{lin2} &= 67675.77342 - 3.670864739*a\\ + \end{align*} \item \begin{align*} \sigma_p= 5Pa\\ @@ -178,7 +179,7 @@ &= |4.967526857 - 0.0005264485258a| \end{align*} Habe keinen Beleg gefunden wie man das Sigma wirklich berechnet. Das hier hab ich mir nur aus dem Kopf gezogen - + %TODO JP muss seine Lösung coden \end{enumerate}