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(b) Bernoulli process: You want to estimate 7, the proportion who identify as Jedi instead of Sith. To accomplish this, you perform an experiment with Jon and Laurits. Jon and Laurits celebrate May the 4th at Forbidden Planet. "May the 4th Be With You". Jon is handing out Sith candy, while Laurits hands out Jedi candy. The customers get to choose which candy they identify with. Your job is to keep track of how many each of them has handed out. You find the numbers in the table below, Jedis in column 2, and Siths in column 3. You find your numbers in the row starting with your candidate number (row 1, left). Example: If you are candidate 547, then Jedi 43 and Sith=20. i. Use Jeffreys' prior hyperparameters for 7. The observations are to be found in the table below. Find the posterior probability distribution for , and draw both pdf the probability distribution. ii. Calculate a 70% interval estimate ("credible interval") for #, draw the CDF for T's probability distribution, and mark the interval estimate on this curve. iii. Dr a confidence curve for 7, and mark 70% interval estimate for on this curve.
Cand. Jedi Sith 201 59 17 202 24 15 203 30 14 204 29 24 205 29 15 206 28 25 207 22 50 208 42 21 209 26 16 210 34 22 211 14 17 212 28 11 213 33 28 214 38 16 215 69 25 216 35 27 217 48 14 218 69 32 219 19 13 220 29 35 221 44 30 222 37 18 223 31 24 224 37 17 225 58 20 226 50 8 227 55 44 228 57 9 229 21 59 230 34 12 231 34 23 232 50 22 233 60 234 27 21 235 38 33 236 50 25 237 42 23 238 32 20 239 20 20 240 44 241 23 15 242 29 37 243 45 22 244 37 29 245 27 25 Cand. Jedi Sith 246 31 15 247 48 46 248 91 24 249 40 19 250 26 28 251 29 30 252 15 14 253 21 24 254 44 44 255 17 23 256 46 257 24 16 258 64 18 9 259 45 260 44 29 261 60 19 262 41 30 263 16 37 264 37 42 265 135 13 266 40 50 267 35 268 33 38 269 42 23 270 23 271 26 18 272 56 37 273 41 21 274 26 27 275 31 15 276 34 25 277 65 17 278 40 29 279 45 34 280 75 21 281 13 14 282 35 12 283 34 47 284 55 29 285 41 286 58 29 287 30 41 288 36 20 289 51 11 290 34 23 Cand. Jedi Sith 291 37 22 42 11 292 293 32 19 294 42 34 295 41 14 296 61 23 297 25 10 298 36 21 299 44 24 300 18 18 301 43 49 24 15 302 303 37 304 305 33 71 19 12 306 27 14 307 37 22 308 43 21 309 74 8 310 60 25 311 32 24 312 73 313 60 23 314 56 24 315 45 28 25 29 316 317 38 28 318 43 10 319 75 8 320 50 321 48 322 25 323 56 324 33 11 325 29 32 326 42 26 327 23 17 44 28 328 329 30 13 330 29 331 32 15 332 29 27 333 42 23 334 28 15 335 33 18 Cand. Jedi Sith 336 70 18 337 60 26 338 43 24 339 36 23 340 48 45 341 35 27 342 67 36 343 47 40 344 36 10 345 54 29 346 47 15 347 32 24 348 32 10 349 21 30 350 53 10 351 38 22 352 28 50 353 29 58 354 16 28 355 48. 30 356 31 48 357 22 358 41 31 359 80 13 360 25 28 361 41 20 362 41 31 363 34 17 364 57 22 365 41 13 366 42 16 367 33 14 368 71 17 18 369 45 370 48 48 371 41 14 23 372 52 373 31 33 374 37 34 375 26 376 20 11 377 19 15 378 49 45 379 44 25 380 30 17
Cand. Jedi Sith 381 27 18 382 35 50 383 31 25 384 41 18 385 53 11 386 27 13 387 29 17 388 38 10 389 40 27 390 19 27 391 19 21 392 38 33 393 29 23 394 35 17 395 53 12 396 44 30 397 20 28 398 38 47 399 29 9 400 40 23 401 32 25 402 26 13 403 25 14 404 53 20 405 37 47 406 53 34 407 21 19 408 67 25 409 35 42 410 57 22 411 31 16 412 25 413 40 20 8 414 34 18 415 23 25 416 54 40 417 52 20 418 18 35 419 50 41 420 26 421 40 25 13 422 36 39 423 24 32 424 32 29 425 18 10 Cand. Jedi Sith 426 52 27 11 27 427 428 34 10 429 34 30 430 29 20 431 41 17 432 21 42 433 48 31 434 73 29 435 40 48 436 35 19 437 36 24 438 35 26 439 36 26 440 30 21 441 25 24 442 31 30 443 41 19 444 66 15 445 27 38 446 40 27 447 45 24 448 28 23 449 39 14 450 53 17 451 49 15 452 30 36 453 33 25 454 37 20 455 38 23 456 39 21 457 51 27 458 35 32 459 24 19 460 23 22 461 46 26 462 39 19 463 37 19 464 28 43 465 25 24 466 53 30 467 57 15 468 37 25 469 55 55 470 54 20 Cand. Jedi Sith 471 30 16 472 29 33 473 44 18. 474 33 25 475 46 24 476 33 19 477 52 42 478 36 21 479 50 13 480 35 19 481 42 28 482 71 19 483 39 33 484 38 20 485 36 28 12 486 24 487 38 19 488 46 13 489 30 16 490 30 30 491 52 42 492 31 19 493 18 31 494 46 16 495 52 26 496 26 497 18 23 498 33 23 499 18. 17 500 50 37 501 41 24 502 43 24 503 46 18 504 11 49 505 35 31 506 47 20 507 30 28 508 29 24 509 30 23 510 57 13 511 47 30 512 62 30 513 27 22 514 27 12 515 49 23 Cand. Jedi Sith 516 32 18 517 85 21 518 44 12 519 37 31 520 25 32 521 27 42 522 53 21 523 27 17 524 39 28 525 25 17 526 35 23 527 40 34 528 26 28 529 38 24 530 66 40 531 41 46 532 35 23 533 39 21 534 14 47 535 25 14 536 34 28 537 25 38 538 23 19 539 23 34 540 19 21 541 18 13 542 42 16 543 50 11 544 105 33 545 546 38 43 15 30 547 43 20 548 52 23 549 34 17 550 30 12 551 23 35 552 101 28 553 63 19 554 38 20 555 24 14 556 22 25 557 27 12 558 32 41 559 32 32 560 41 38