Rikuti

intr

leerlaufspannung

Integrale 

Totale Differenzierbarkeit

Mittelwertsatz

Mathe I

euklidischer Algorithmus

Brückenschaltung

Lineare Algebra 

QR-Zerlegung

Cholesky-Zerlegung

Stützmpment

Simplex Algorithmus

Optimierung in mehreren Variablen + Envelop Theorem 

Exterma Untersuchung

Basiswechselmatrix

Differenzenverstärker

übertragungsfunktion

Darstellungsmatrizen in neuer Basis darstellen

Basis wechsel, Transformationsmatrizen

Monotieverhalten

Cauchy-Produktformel

physik

elastischer stoss

lösbarkeit einer Matrix

kinematik

impuls

kugelkoordinaten une zylinderkoordinaten 

Matrix

Integralgleichung

kettenregel

Lösbarkeit einer Matrix

Glechgewicht

Schiefe Ebene

Cauchy Verdichtungssatz 

Schaltvorgänge

Singulärwertzerlegung

Spann

Lineares Gleichungssystem

spannung

Basis bestimmen

Fourier-Reihen

Unterschied In/Homogen

Gruppen

lineare abbildung 

quadratische ergänzung

basis 

Bild & Urbild

Zweigstromanalyse

Transistor als Thermometer

Investment

Teilfolgen

Epsilon Delta Kriterium

prinzip der virtuellen verrückung 

Linear Kombination

Cholesky Zerlegung

Polynomfunktionen beschreiben

Teilchenphysik und Festkörperphysik

test

Regel von de L'Hopital

KRAFT

Grenzwert Funktion 

Folgenkriterium

ϵ-δ Kriterium 

Beweis Stetigkeit 

Basiswechselsatz

Vorderrad fahradgabel lagerkräfte berechnen 

Spannungsregelung

Test

Induktion 

Jordan-Normalform

Inverse einer Matrix

Gleichmäßige Stetigkeit

addition

Stationäre Stoffübertragung

komplexe Ungleichungen 

Rekursive Folgen

Exponentialreihe

restglied

Newton Verfahren

Randwertaufgabe

Numerische Integration: Trapez- und Simpsonregel

dualräume

Dualraum

Komplexe Nullstellen

Chemie

Folgedefinition des Funktionslimes

Grenzwerte und Stetigkeit 

Komplexe Zahlen

Direkte Summe 

Exponentielle Verzinsung

Tilgungsrechnung

Abschreibungsrechnung

Zins- und Barwertrechnung

<p>- Binomialverteilung \( \mathrm{B}(\mathrm{n}, 0.5) \quad \sum \mathrm{p}_{\mathrm{k}}=1 \)</p>
<p>- Binomialverteilung \( \mathrm{B}(\mathrm{n}, 0.5) \quad \mathbf{E} \xi=\mathrm{np}=\frac{\mathrm{n}}{2} \)</p>
<p>- Hypergeometrische Vert. \( M=2 n, \quad M_{1}=M_{2}=n \quad \sum p_{k}=1 \)</p>


<p>Man zeige mit Mitteln der Wahrscheinlichkeitsrechnung</p>
<ol style="list-style-type: lower-alpha;">
<li>\( \sum_{k=0}^{n}\left(\begin{array}{l}n \\ k\end{array}\right)=2^{n} \)</li>
<li>\( \sum_{k=0}^{n} k\left(\begin{array}{l}n \\ k\end{array}\right)=n 2^{n-1} \)</li>
<li>\( \sum_{k=0}^{n}\left(\begin{array}{l}n \\ k\end{array}\right)^{2}=\left(\begin{array}{c}2 n \\ n\end{array}\right) \).</li>
</ol>

<p>Man zeige mit Mitteln der Wahrscheinlichkeitsrechnung</p>
<ol style="list-style-type: lower-alpha;">
<li><mjx-container class="MathJax" jax="SVG"><svg alt=" \sum_{k=0}^{n}\left(\begin{array}{l}n \\ k\end{array}\right)=2^{n} " style="vertical-align: -2.149ex" xmlns="http://www.w3.org/2000/svg" width="15.816ex" height="5.43ex" role="img" focusable="false" viewBox="0 -1450 6990.6 2400" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-108-TEX-SO-2211" d="M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z"></path><path id="MJX-108-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-108-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path id="MJX-108-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-108-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-108-TEX-S3-28" d="M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z"></path><path id="MJX-108-TEX-S3-29" d="M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z"></path><path id="MJX-108-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="munderover"><g data-mml-node="mo"><use data-c="2211" xlink:href="#MJX-108-TEX-SO-2211"></use></g><g data-mml-node="TeXAtom" transform="translate(1089,477.1) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-108-TEX-I-1D45B"></use></g></g><g data-mml-node="TeXAtom" transform="translate(1089,-285.4) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D458" xlink:href="#MJX-108-TEX-I-1D458"></use></g><g data-mml-node="mo" transform="translate(521,0)"><use data-c="3D" xlink:href="#MJX-108-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(1299,0)"><use data-c="30" xlink:href="#MJX-108-TEX-N-30"></use></g></g></g><g data-mml-node="mrow" transform="translate(2577.8,0)"><g data-mml-node="mo" transform="translate(0 -0.5)"><use data-c="28" xlink:href="#MJX-108-TEX-S3-28"></use></g><g data-mml-node="mtable" transform="translate(736,0)"><g data-mml-node="mtr" transform="translate(0,700)"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-108-TEX-I-1D45B"></use></g></g></g><g data-mml-node="mtr" transform="translate(0,-700)"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D458" xlink:href="#MJX-108-TEX-I-1D458"></use></g></g></g></g><g data-mml-node="mo" transform="translate(1336,0) translate(0 -0.5)"><use data-c="29" xlink:href="#MJX-108-TEX-S3-29"></use></g></g><g data-mml-node="mo" transform="translate(4927.5,0)"><use data-c="3D" xlink:href="#MJX-108-TEX-N-3D"></use></g><g data-mml-node="msup" transform="translate(5983.3,0)"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-108-TEX-N-32"></use></g><g data-mml-node="TeXAtom" transform="translate(533,363) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-108-TEX-I-1D45B"></use></g></g></g></g></g></svg></mjx-container></li>
<li><mjx-container class="MathJax" jax="SVG"><svg alt=" \sum_{k=0}^{n} k\left(\begin{array}{l}n \\ k\end{array}\right)=n 2^{n-1} " style="vertical-align: -2.149ex" xmlns="http://www.w3.org/2000/svg" width="20.774ex" height="5.43ex" role="img" focusable="false" viewBox="0 -1450 9181.9 2400" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-109-TEX-SO-2211" d="M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z"></path><path id="MJX-109-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-109-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path id="MJX-109-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-109-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-109-TEX-S3-28" d="M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z"></path><path id="MJX-109-TEX-S3-29" d="M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z"></path><path id="MJX-109-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-109-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-109-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="munderover"><g data-mml-node="mo"><use data-c="2211" xlink:href="#MJX-109-TEX-SO-2211"></use></g><g data-mml-node="TeXAtom" transform="translate(1089,477.1) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-109-TEX-I-1D45B"></use></g></g><g data-mml-node="TeXAtom" transform="translate(1089,-285.4) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D458" xlink:href="#MJX-109-TEX-I-1D458"></use></g><g data-mml-node="mo" transform="translate(521,0)"><use data-c="3D" xlink:href="#MJX-109-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(1299,0)"><use data-c="30" xlink:href="#MJX-109-TEX-N-30"></use></g></g></g><g data-mml-node="mi" transform="translate(2577.8,0)"><use data-c="1D458" xlink:href="#MJX-109-TEX-I-1D458"></use></g><g data-mml-node="mrow" transform="translate(3265.4,0)"><g data-mml-node="mo" transform="translate(0 -0.5)"><use data-c="28" xlink:href="#MJX-109-TEX-S3-28"></use></g><g data-mml-node="mtable" transform="translate(736,0)"><g data-mml-node="mtr" transform="translate(0,700)"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-109-TEX-I-1D45B"></use></g></g></g><g data-mml-node="mtr" transform="translate(0,-700)"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D458" xlink:href="#MJX-109-TEX-I-1D458"></use></g></g></g></g><g data-mml-node="mo" transform="translate(1336,0) translate(0 -0.5)"><use data-c="29" xlink:href="#MJX-109-TEX-S3-29"></use></g></g><g data-mml-node="mo" transform="translate(5615.2,0)"><use data-c="3D" xlink:href="#MJX-109-TEX-N-3D"></use></g><g data-mml-node="mi" transform="translate(6671,0)"><use data-c="1D45B" xlink:href="#MJX-109-TEX-I-1D45B"></use></g><g data-mml-node="msup" transform="translate(7271,0)"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-109-TEX-N-32"></use></g><g data-mml-node="TeXAtom" transform="translate(533,363) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-109-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(600,0)"><use data-c="2212" xlink:href="#MJX-109-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(1378,0)"><use data-c="31" xlink:href="#MJX-109-TEX-N-31"></use></g></g></g></g></g></svg></mjx-container></li>
<li><mjx-container class="MathJax" jax="SVG"><svg alt=" \sum_{k=0}^{n}\left(\begin{array}{l}n \\ k\end{array}\right)^{2}=\left(\begin{array}{c}2 n \\ n\end{array}\right) " style="vertical-align: -2.149ex" xmlns="http://www.w3.org/2000/svg" width="20.344ex" height="5.878ex" role="img" focusable="false" viewBox="0 -1648 8991.9 2598" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-110-TEX-SO-2211" d="M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z"></path><path id="MJX-110-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-110-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path id="MJX-110-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-110-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-110-TEX-S3-28" d="M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z"></path><path id="MJX-110-TEX-S3-29" d="M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z"></path><path id="MJX-110-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="munderover"><g data-mml-node="mo"><use data-c="2211" xlink:href="#MJX-110-TEX-SO-2211"></use></g><g data-mml-node="TeXAtom" transform="translate(1089,477.1) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-110-TEX-I-1D45B"></use></g></g><g data-mml-node="TeXAtom" transform="translate(1089,-285.4) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D458" xlink:href="#MJX-110-TEX-I-1D458"></use></g><g data-mml-node="mo" transform="translate(521,0)"><use data-c="3D" xlink:href="#MJX-110-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(1299,0)"><use data-c="30" xlink:href="#MJX-110-TEX-N-30"></use></g></g></g><g data-mml-node="msup" transform="translate(2577.8,0)"><g data-mml-node="mrow"><g data-mml-node="mo" transform="translate(0 -0.5)"><use data-c="28" xlink:href="#MJX-110-TEX-S3-28"></use></g><g data-mml-node="mtable" transform="translate(736,0)"><g data-mml-node="mtr" transform="translate(0,700)"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-110-TEX-I-1D45B"></use></g></g></g><g data-mml-node="mtr" transform="translate(0,-700)"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D458" xlink:href="#MJX-110-TEX-I-1D458"></use></g></g></g></g><g data-mml-node="mo" transform="translate(1336,0) translate(0 -0.5)"><use data-c="29" xlink:href="#MJX-110-TEX-S3-29"></use></g></g><g data-mml-node="TeXAtom" transform="translate(2105,1177.1) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-110-TEX-N-32"></use></g></g></g><g data-mml-node="mo" transform="translate(5364.1,0)"><use data-c="3D" xlink:href="#MJX-110-TEX-N-3D"></use></g><g data-mml-node="mrow" transform="translate(6419.9,0)"><g data-mml-node="mo" transform="translate(0 -0.5)"><use data-c="28" xlink:href="#MJX-110-TEX-S3-28"></use></g><g data-mml-node="mtable" transform="translate(736,0)"><g data-mml-node="mtr" transform="translate(0,700)"><g data-mml-node="mtd"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-110-TEX-N-32"></use></g><g data-mml-node="mi" transform="translate(500,0)"><use data-c="1D45B" xlink:href="#MJX-110-TEX-I-1D45B"></use></g></g></g><g data-mml-node="mtr" transform="translate(0,-700)"><g data-mml-node="mtd" transform="translate(250,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-110-TEX-I-1D45B"></use></g></g></g></g><g data-mml-node="mo" transform="translate(1836,0) translate(0 -0.5)"><use data-c="29" xlink:href="#MJX-110-TEX-S3-29"></use></g></g></g></g></svg></mjx-container>.</li>
</ol>

Dies ist eine interaktive Aufgabe zu: Rikuti mit praktischen Tipps zum Lösen und einer Zusammenfassung der nötigen Theorie

Stochastik - Rikuti | Aufgabe mit Lösung

Aufgabenstellung:

Lösungsweg:

Lösung: