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A10.4 GAUSSIAN DISTRIBUTION
A10.4 GAUSSIAN DISTRIBUTION
- Former user (Deleted)
Owned by Former user (Deleted)
It is an ordinary Gaussian (Normal) distribution defined by mean m and standard deviation σ values:
=%5cfrac%7b1%7d%7b%5csqrt%7b2%5cpi %5csigma %7d%7d%5cexp %5cleft( -%5cfrac%7b%7b%7b%5cleft( x-m %5cright)%7d%5e%7b2%7d%7d%7d%7b2%5csigma %7d %5cright)%5cend%7barray%7d%3c/title%3e %3cdefs aria-hidden='true'%3e %3cpath stroke-width='1' id='E1-MJMATHI-47' d='M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q492 659 471 656T418 643T357 615T294 567T236 496T189 394T158 260Q156 242 156 221Q156 173 170 136T206 79T256 45T308 28T353 24Q407 24 452 47T514 106Q517 114 529 161T541 214Q541 222 528 224T468 227H431Q425 233 425 235T427 254Q431 267 437 273H454Q494 271 594 271Q634 271 659 271T695 272T707 272Q721 272 721 263Q721 261 719 249Q714 230 709 228Q706 227 694 227Q674 227 653 224Q646 221 643 215T629 164Q620 131 614 108Q589 6 586 3Q584 1 581 1Q571 1 553 21T530 52Q530 53 528 52T522 47Q448 -22 322 -22Q201 -22 126 55T50 252Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMAIN-28' d='M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMATHI-6D' d='M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMAIN-2C' d='M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMATHI-3C3' d='M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMAIN-29' d='M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMAIN-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'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMAIN-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'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMAIN-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'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMATHI-3C0' d='M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMAIN-221A' d='M95 178Q89 178 81 186T72 200T103 230T169 280T207 309Q209 311 212 311H213Q219 311 227 294T281 177Q300 134 312 108L397 -77Q398 -77 501 136T707 565T814 786Q820 800 834 800Q841 800 846 794T853 782V776L620 293L385 -193Q381 -200 366 -200Q357 -200 354 -197Q352 -195 256 15L160 225L144 214Q129 202 113 190T95 178Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMAIN-65' d='M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMAIN-78' d='M201 0Q189 3 102 3Q26 3 17 0H11V46H25Q48 47 67 52T96 61T121 78T139 96T160 122T180 150L226 210L168 288Q159 301 149 315T133 336T122 351T113 363T107 370T100 376T94 379T88 381T80 383Q74 383 44 385H16V431H23Q59 429 126 429Q219 429 229 431H237V385Q201 381 201 369Q201 367 211 353T239 315T268 274L272 270L297 304Q329 345 329 358Q329 364 327 369T322 376T317 380T310 384L307 385H302V431H309Q324 428 408 428Q487 428 493 431H499V385H492Q443 385 411 368Q394 360 377 341T312 257L296 236L358 151Q424 61 429 57T446 50Q464 46 499 46H516V0H510H502Q494 1 482 1T457 2T432 2T414 3Q403 3 377 3T327 1L304 0H295V46H298Q309 46 320 51T331 63Q331 65 291 120L250 175Q249 174 219 133T185 88Q181 83 181 74Q181 63 188 55T206 46Q208 46 208 23V0H201Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMAIN-70' d='M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMAIN-2212' d='M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMATHI-78' d='M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJSZ3-28' 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'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJSZ3-29' 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'%3e%3c/path%3e %3c/defs%3e %3cg stroke='currentColor' fill='currentColor' stroke-width='0' transform='matrix(1 0 0 -1 0 0)' aria-hidden='true'%3e %3cg transform='translate(167%2c0)'%3e %3cg transform='translate(-11%2c0)'%3e %3cuse xlink:href='%23E1-MJMATHI-47' x='0' y='0'%3e%3c/use%3e %3cg transform='translate(953%2c0)'%3e %3cuse xlink:href='%23E1-MJMAIN-28' x='0' y='0'%3e%3c/use%3e %3cuse xlink:href='%23E1-MJMATHI-6D' x='389' y='0'%3e%3c/use%3e %3cuse xlink:href='%23E1-MJMAIN-2C' x='1268' y='0'%3e%3c/use%3e %3cuse xlink:href='%23E1-MJMATHI-3C3' x='1713' y='0'%3e%3c/use%3e %3cuse xlink:href='%23E1-MJMAIN-29' x='2285' y='0'%3e%3c/use%3e %3c/g%3e %3cuse xlink:href='%23E1-MJMAIN-3D' x='3906' y='0'%3e%3c/use%3e %3cg transform='translate(4684%2c0)'%3e %3cg transform='translate(397%2c0)'%3e %3crect stroke='none' width='1873' height='60' x='0' y='220'%3e%3c/rect%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMAIN-31' x='1074' y='629'%3e%3c/use%3e %3cg transform='translate(60%2c-562)'%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMAIN-221A' x='0' y='11'%3e%3c/use%3e %3crect stroke='none' width='1164' height='42' x='589' y='532'%3e%3c/rect%3e %3cg transform='translate(589%2c0)'%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMAIN-32' x='0' y='0'%3e%3c/use%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMATHI-3C0' x='500' y='0'%3e%3c/use%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMATHI-3C3' x='1074' y='0'%3e%3c/use%3e %3c/g%3e %3c/g%3e %3c/g%3e %3c/g%3e %3cg transform='translate(7076%2c0)'%3e %3cuse xlink:href='%23E1-MJMAIN-65'%3e%3c/use%3e %3cuse xlink:href='%23E1-MJMAIN-78' x='444' y='0'%3e%3c/use%3e %3cuse xlink:href='%23E1-MJMAIN-70' x='973' y='0'%3e%3c/use%3e %3c/g%3e %3cg transform='translate(8605%2c0)'%3e %3cuse xlink:href='%23E1-MJSZ3-28'%3e%3c/use%3e %3cuse xlink:href='%23E1-MJMAIN-2212' x='736' y='0'%3e%3c/use%3e %3cg transform='translate(1515%2c0)'%3e %3cg transform='translate(120%2c0)'%3e %3crect stroke='none' width='2605' height='60' x='0' y='220'%3e%3c/rect%3e %3cg transform='translate(60%2c622)'%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMAIN-28' x='0' y='0'%3e%3c/use%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMATHI-78' x='389' y='0'%3e%3c/use%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMAIN-2212' x='962' y='0'%3e%3c/use%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMATHI-6D' x='1740' y='0'%3e%3c/use%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMAIN-29' x='2619' y='0'%3e%3c/use%3e %3cuse transform='scale(0.574)' xlink:href='%23E1-MJMAIN-32' x='3705' y='538'%3e%3c/use%3e %3c/g%3e %3cg transform='translate(923%2c-417)'%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMAIN-32' x='0' y='0'%3e%3c/use%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMATHI-3C3' x='500' y='0'%3e%3c/use%3e %3c/g%3e %3c/g%3e %3c/g%3e %3cuse xlink:href='%23E1-MJSZ3-29' x='4360' y='-1'%3e%3c/use%3e %3c/g%3e %3c/g%3e %3c/g%3e %3c/g%3e %3c/svg%3e)
(Eq. 141)
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Figure 404: Gaussian distribution: parameters (left) PDF (right)