class: center, middle, title-slide .title[ # Practical 6 ] .author[ ### Olivier Gimenez ] .date[ ### last updated: 2023-11-11 ] --- ## Working with the MCMC outputs * From the values you generated in the posterior distribution of parameter say `\(\theta\)`, you may get the posterior distribution of any function of `\(\theta\)` * For example, back to the stork Bayesian analysis, get the posterior distribution of `\(b^2_{rain} + \cos(b_{temp})\)` --- ## Solutions --- * Evaluate the function for each MCMC iteration ```r stupid <- res[,'b.rain']^2 + cos(res[,'b.temp']) ``` .tiny-font[ ```r stupid ``` ``` ## [1] 1.0533654 1.0345638 1.0523413 1.0421076 1.0794384 1.0646006 1.0592698 ## [8] 1.0320126 1.0251255 1.0271967 1.0379850 1.0367091 1.0240317 1.0240360 ## [15] 1.0332134 1.0302682 1.0236301 1.0528568 1.0245898 1.0364347 1.0396234 ## [22] 1.0339663 1.0274247 1.0129775 1.0120239 1.0149246 1.0109520 1.0045903 ## [29] 1.0047252 1.0067256 1.0081930 1.0131398 1.0134849 1.0418373 1.0475406 ## [36] 1.0486655 1.0258187 1.0376803 1.0389084 1.0428197 1.0381890 1.0297020 ## [43] 1.0265459 1.0305688 1.0280045 1.0203155 1.0216109 1.0337297 1.0465033 ## [50] 1.0307128 1.0301963 1.0405842 1.0362545 1.0202438 1.0284384 1.0167877 ## [57] 1.0173963 1.0219457 1.0275491 1.0369082 1.0259660 1.0171182 1.0164563 ## [64] 1.0167814 1.0166253 1.0183313 1.0113273 1.0104482 1.0100595 1.0216466 ## [71] 1.0241985 1.0374226 1.0155275 1.0214522 1.0205117 1.0259742 1.0321411 ## [78] 1.0290169 1.0178231 1.0320309 1.0397650 1.0282952 1.0233118 1.0100424 ## [85] 1.0036218 1.0019575 1.0012685 1.0030554 1.0057290 1.0114607 1.0251020 ## [92] 1.0345374 1.0151870 1.0066028 1.0104423 1.0144381 1.0092053 1.0115044 ## [99] 1.0086589 1.0061894 1.0029841 1.0032379 1.0030377 0.9997910 1.0011945 ## [106] 1.0020388 1.0014096 1.0017458 1.0100996 1.0283754 1.0103464 1.0214325 ## [113] 1.0227425 1.0358386 1.0367818 1.0366494 1.0231540 1.0197731 1.0173119 ## [120] 1.0123906 1.0115854 1.0125292 1.0176417 1.0068692 1.0137827 1.0172534 ## [127] 1.0376307 1.0321051 1.0239103 1.0254700 1.0327793 1.0402292 1.0545173 ## [134] 1.0410189 1.0195214 1.0309736 1.0145214 1.0170167 1.0335616 1.0426545 ## [141] 1.0371352 1.0280224 1.0323649 1.0538453 1.0574698 1.0589001 1.0582822 ## [148] 1.0334254 1.0350472 1.0334107 1.0230310 1.0326354 1.0397817 1.0225924 ## [155] 1.0421716 1.0438446 1.0397856 1.0249006 1.0145880 1.0087748 1.0046620 ## [162] 1.0109485 1.0081199 1.0135283 1.0125224 1.0102458 1.0084061 1.0089609 ## [169] 1.0034488 1.0045580 1.0060953 1.0149125 1.0213077 1.0213645 1.0174894 ## [176] 1.0158983 1.0116947 1.0035940 1.0060632 1.0075958 1.0035165 1.0108540 ## [183] 1.0385696 1.0363111 1.0360054 1.0434782 1.0321639 1.0157583 1.0210798 ## [190] 1.0224733 1.0159742 1.0155933 1.0081904 1.0043160 1.0136643 1.0136738 ## [197] 1.0228176 1.0293946 1.0259572 1.0337162 1.0271312 1.0461180 1.0385637 ## [204] 1.0301836 1.0406078 1.0247131 1.0354494 1.0464538 1.0400268 1.0529028 ## [211] 1.0682486 1.0642032 1.0682300 1.0856471 1.0803462 1.0566876 1.0766756 ## [218] 1.0768169 1.0889456 1.0712039 1.0920360 1.1198815 1.1207742 1.0995465 ## [225] 1.0664279 1.0706507 1.0497512 1.0535564 1.0697352 1.0412604 1.0350590 ## [232] 1.0263685 1.0196309 1.0177514 1.0086108 1.0149171 1.0109429 1.0113288 ## [239] 1.0153343 1.0213934 1.0355230 1.0378025 1.0378244 1.0441893 1.0344786 ## [246] 1.0323300 1.0487707 1.0293352 1.0116244 1.0090538 1.0089405 1.0263295 ## [253] 1.0142367 1.0140356 1.0090700 1.0144727 1.0137391 1.0048098 1.0033775 ## [260] 1.0003471 1.0036451 1.0116166 1.0155966 1.0129261 1.0151922 1.0203037 ## [267] 1.0259816 1.0162522 1.0102952 1.0085992 1.0075371 1.0109393 1.0136238 ## [274] 1.0190952 1.0208966 1.0273916 1.0359595 1.0255050 1.0321481 1.0509112 ## [281] 1.0493223 1.0678841 1.0709774 1.0733695 1.1040627 1.0682455 1.0647492 ## [288] 1.0759089 1.0771458 1.0663279 1.0594970 1.0530126 1.0739676 1.0880891 ## [295] 1.0929735 1.0514396 1.0521348 1.0530472 1.0533708 1.0799137 1.0785072 ## [302] 1.0816436 1.0874580 1.0848161 1.0607797 1.0610397 1.0620769 1.0764389 ## [309] 1.0537786 1.0795432 1.0765960 1.0787428 1.0499656 1.0467417 1.0421976 ## [316] 1.0248042 1.0220427 1.0107257 1.0125240 1.0149978 1.0145370 1.0192947 ## [323] 1.0202781 1.0046189 1.0006989 1.0031598 1.0091055 1.0039752 1.0036665 ## [330] 1.0022249 1.0053684 0.9969920 0.9998726 1.0010463 1.0059667 1.0054092 ## [337] 1.0135320 1.0069465 1.0094429 1.0051154 1.0065878 1.0037471 1.0080377 ## [344] 1.0078919 1.0140235 1.0175068 1.0180606 1.0174835 1.0173930 1.0092791 ## [351] 1.0076841 0.9967999 0.9973639 0.9933033 0.9959347 0.9953237 0.9944612 ## [358] 0.9963925 1.0071884 1.0016581 0.9985857 1.0003015 0.9940147 1.0046022 ## [365] 1.0081384 1.0061017 1.0330597 1.0238045 1.0274431 1.0266455 1.0157763 ## [372] 1.0230523 1.0140875 1.0091156 1.0147773 1.0106197 1.0075139 1.0179199 ## [379] 1.0308838 1.0431695 1.0518655 1.0480756 1.0179154 1.0122030 1.0133729 ## [386] 1.0143519 1.0222491 1.0207326 1.0256866 1.0177522 1.0194632 1.0092110 ## [393] 1.0045934 1.0134524 1.0128432 1.0087859 1.0078060 1.0113984 1.0066256 ## [400] 1.0138230 1.0111833 1.0072703 1.0053258 1.0108595 1.0197189 1.0206563 ## [407] 1.0083513 1.0101556 1.0061853 1.0095858 1.0196557 1.0180873 1.0170853 ## [414] 1.0138477 1.0176111 1.0208441 1.0097025 1.0082196 1.0057986 1.0036836 ## [421] 1.0055176 1.0015033 1.0078725 1.0036648 1.0112496 1.0216667 1.0192002 ## [428] 1.0147904 1.0161535 1.0196525 1.0158259 1.0304751 1.0687452 1.0592870 ## [435] 1.0381039 1.0366093 1.0422138 1.0506358 1.0573639 1.0908266 1.0724755 ## [442] 1.0809306 1.1088689 1.0723776 1.0655822 1.0387364 1.0363539 1.0278372 ## [449] 1.0256862 1.0177731 1.0088799 1.0159226 1.0204338 1.0276334 1.0357546 ## [456] 1.0349186 1.0273314 1.0408932 1.0630644 1.0529472 1.0516754 1.0444881 ## [463] 1.0297355 1.0105912 1.0110722 1.0166362 1.0263864 1.0392661 1.0475233 ## [470] 1.0574363 1.0497815 1.0318515 1.0293361 1.0387300 1.0385233 1.0279800 ## [477] 1.0224520 1.0311069 1.0251678 1.0237571 1.0220703 1.0235085 1.0145105 ## [484] 1.0112122 1.0231943 1.0312100 1.0267082 1.0468987 1.0352916 1.0539744 ## [491] 1.0629751 1.0621567 1.0555315 1.0608657 1.0763215 1.0750786 1.0851748 ## [498] 1.0582366 1.0633232 1.0925708 1.0910112 1.0600688 1.0447274 1.0281923 ## [505] 1.0297512 1.0286393 1.0360260 1.0360117 1.0214691 1.0201658 1.0431419 ## [512] 1.0386481 1.0484303 1.0254231 1.0195003 1.0313228 1.0150606 1.0132253 ## [519] 1.0191718 1.0112997 1.0102376 1.0078922 1.0143813 1.0074963 1.0063556 ## [526] 1.0086175 1.0178813 1.0417520 1.0375772 1.0473515 1.0403449 1.0332129 ## [533] 1.0319617 1.0310129 1.0423912 1.0417209 1.0364011 1.0265191 1.0279976 ## [540] 1.0252774 1.0412280 1.0400608 1.0302771 1.0446482 1.0397917 1.0464195 ## [547] 1.0250143 1.0302329 1.0228268 1.0277094 1.0221383 1.0305601 1.0313945 ## [554] 1.0301529 1.0343681 1.0366369 1.0272915 1.0416518 1.0456956 1.0697021 ## [561] 1.0891158 1.0929002 1.0985937 1.1154292 1.0900939 1.0706580 1.0920648 ## [568] 1.1130882 1.1235453 1.1320564 1.1297300 1.1177808 1.0786976 1.0593580 ## [575] 1.0487801 1.0553620 1.0445515 1.0397271 1.0411098 1.0447934 1.0393943 ## [582] 1.0288512 1.0465878 1.0515701 1.0666166 1.0815042 1.0876789 1.0823005 ## [589] 1.0760662 1.0517509 1.0641637 1.0745327 1.0451401 1.0343009 1.0355580 ## [596] 1.0303078 1.0204945 1.0448155 1.0643193 1.0572011 1.0519011 1.0505975 ## [603] 1.0393473 1.0572018 1.0428109 1.0476373 1.0444013 1.0353097 1.0318918 ## [610] 1.0209279 1.0236578 1.0155279 1.0181434 1.0347219 1.0283025 1.0397391 ## [617] 1.0585963 1.0745495 1.0634347 1.0551993 1.0304628 1.0293584 1.0226960 ## [624] 1.0284163 1.0538134 1.0742695 1.0899191 1.0680591 1.0743910 1.0557674 ## [631] 1.0730958 1.0658692 1.0593833 1.0423557 1.0396722 1.0458107 1.0395674 ## [638] 1.0361561 1.0290582 1.0199823 1.0153056 1.0205492 1.0115949 1.0231776 ## [645] 1.0362997 1.0270200 1.0064801 1.0176033 1.0329257 1.0383044 1.0347033 ## [652] 1.0227528 1.0182854 1.0240330 1.0102887 1.0147914 1.0258208 1.0281331 ## [659] 1.0379879 1.0359355 1.0370352 1.0377224 1.0232061 1.0186599 1.0142286 ## [666] 1.0083050 1.0049261 1.0110315 1.0167755 1.0183317 1.0220203 1.0199342 ## [673] 1.0197040 1.0154641 1.0145207 1.0176907 1.0128027 1.0117486 1.0236913 ## [680] 1.0326157 1.0256345 1.0096508 1.0134419 1.0171086 1.0363330 1.0484190 ## [687] 1.0434530 1.0354420 1.0178545 1.0122225 1.0139480 1.0147964 1.0072992 ## [694] 1.0011437 1.0091659 1.0115080 1.0147163 1.0138360 1.0208553 1.0146067 ## [701] 1.0075533 1.0059258 1.0122980 1.0138830 1.0163008 1.0115808 1.0139324 ## [708] 1.0279020 1.0278890 1.0211001 1.0218217 1.0249166 1.0191765 1.0261533 ## [715] 1.0313698 1.0318243 1.0216437 1.0166980 1.0095701 1.0084513 1.0164096 ## [722] 1.0117602 1.0196900 1.0193268 1.0354687 1.0317377 1.0334043 1.0392742 ## [729] 1.0291670 1.0419664 1.0538325 1.0522878 1.0347656 1.0568801 1.0460249 ## [736] 1.0678274 1.0667369 1.0629515 1.0779610 1.0859887 1.0643230 1.0555142 ## [743] 1.0698381 1.0719258 1.0899078 1.0546545 1.0543371 1.0341687 1.0346764 ## [750] 1.0387772 1.0376257 1.0188132 1.0168729 1.0281073 1.0272436 1.0162432 ## [757] 1.0180277 1.0336774 1.0153977 1.0274831 1.0305683 1.0601083 1.0579862 ## [764] 1.0498022 1.0377545 1.0519451 1.0195647 1.0345450 1.0586363 1.0814183 ## [771] 1.0587263 1.0692168 1.0778976 1.0858732 1.0868095 1.0791170 1.0897519 ## [778] 1.0671113 1.0470146 1.0294482 1.0418492 1.0443192 1.0576247 1.0487490 ## [785] 1.0531374 1.0476032 1.0384172 1.0431972 1.0291392 1.0300515 1.0387278 ## [792] 1.0289412 1.0171123 1.0226831 1.0085165 1.0132812 1.0265952 1.0233470 ## [799] 1.0220349 1.0147975 1.0078551 1.0069489 1.0081262 1.0042259 1.0047059 ## [806] 1.0147649 1.0068072 1.0121736 1.0103180 1.0047152 1.0034615 1.0137587 ## [813] 1.0040219 1.0030718 1.0075590 1.0035561 1.0069259 1.0074825 1.0028991 ## [820] 1.0048625 1.0058678 1.0002192 1.0012452 1.0008000 1.0012864 1.0126155 ## [827] 1.0099625 1.0032526 1.0027237 1.0024382 1.0041889 0.9975842 0.9976521 ## [834] 0.9994183 0.9973628 0.9970364 0.9976382 0.9984191 1.0004190 1.0013079 ## [841] 1.0004869 0.9992339 0.9982455 0.9978644 0.9996813 1.0031964 0.9973907 ## [848] 0.9978587 0.9979846 1.0104101 1.0198596 1.0236677 1.0362039 1.0417571 ## [855] 1.0381601 1.0378912 1.0202317 1.0243802 1.0224029 1.0237222 1.0349790 ## [862] 1.0358974 1.0229750 1.0213893 1.0239612 1.0307685 1.0321314 1.0361705 ## [869] 1.0456713 1.0684391 1.0791010 1.0618729 1.0497281 1.0508888 1.0400662 ## [876] 1.0432680 1.0403211 1.0229429 1.0236631 1.0231218 1.0152225 1.0113597 ## [883] 1.0130306 1.0421060 1.0497787 1.0475652 1.0598920 1.0694358 1.0659355 ## [890] 1.0650737 1.0452420 1.0355990 1.0329361 1.0209523 1.0249941 1.0275631 ## [897] 1.0362558 1.0416896 1.0410485 1.0176660 1.0178359 1.0122963 1.0190513 ## [904] 1.0220489 1.0296337 1.0290816 1.0269503 1.0334996 1.0466273 1.0448543 ## [911] 1.0466734 1.0509685 1.0508128 1.0303802 1.0219732 1.0227163 1.0290521 ## [918] 1.0201968 1.0139294 1.0156138 1.0094192 1.0066960 1.0128836 1.0125148 ## [925] 1.0288764 1.0159816 1.0189110 1.0094708 1.0094016 1.0025402 1.0067470 ## [932] 1.0112566 1.0081963 1.0158234 1.0116351 1.0103536 1.0193333 1.0129759 ## [939] 1.0101422 1.0276955 1.0488732 1.0432052 1.0334474 1.0265960 1.0272400 ## [946] 1.0170230 1.0112559 1.0024751 1.0062137 1.0146954 1.0089862 1.0106559 ## [953] 1.0111597 0.9999384 1.0220755 1.0183214 1.0141071 1.0163350 1.0272931 ## [960] 1.0344082 1.0443652 1.0430887 1.0239741 1.0217025 1.0297498 1.0190860 ## [967] 1.0270424 1.0176082 1.0153250 1.0227615 1.0293448 1.0192808 1.0110002 ## [974] 1.0111081 1.0108258 1.0183001 1.0134670 1.0031217 1.0014562 1.0052364 ## [981] 1.0077230 1.0288765 1.0171342 1.0153742 1.0352868 1.0472321 1.0508913 ## [988] 1.0517109 1.0579932 1.0359414 1.0371429 1.0375388 1.0475992 1.0306866 ## [995] 1.0553394 1.0540373 1.0464687 1.0403930 1.0202744 1.0182719 1.0494434 ## [1002] 1.0012958 0.9907198 0.9926892 0.9971191 0.9939430 0.9866369 0.9905762 ## [1009] 0.9985522 1.0005269 1.0135345 1.0163397 1.0271071 1.0304708 1.0303212 ## [1016] 1.0234156 1.0170851 1.0109373 1.0155583 1.0148374 1.0003402 1.0121154 ## [1023] 1.0108649 1.0300200 1.0439614 1.0453732 1.0384573 1.0420870 1.0288811 ## [1030] 1.0460963 1.0511699 1.0539142 1.0595285 1.0500815 1.0300044 1.0520639 ## [1037] 1.0497595 1.0644129 1.0690299 1.0587852 1.0572449 1.0535731 1.0416307 ## [1044] 1.0492810 1.0461870 1.0436415 1.0320460 1.0282674 1.0425874 1.0374044 ## [1051] 1.0329852 1.0141301 1.0196164 1.0102864 1.0161973 1.0164603 1.0202895 ## [1058] 1.0207477 1.0222195 1.0228443 1.0257309 1.0312823 1.0223696 1.0273313 ## [1065] 1.0090332 1.0237857 1.0317365 1.0463761 1.0509489 1.0410069 1.0482588 ## [1072] 1.0447157 1.0454519 1.0728646 1.0475121 1.0474568 1.0553597 1.0583099 ## [1079] 1.0392377 1.0330295 1.0338356 1.0425941 1.0662724 1.0644135 1.0494846 ## [1086] 1.0445103 1.0291534 1.0341107 1.0219647 1.0247269 1.0234280 1.0238097 ## [1093] 1.0220432 1.0270708 1.0284612 1.0140962 1.0243952 1.0122505 1.0188003 ## [1100] 1.0216218 1.0261046 1.0238737 1.0204211 1.0080014 1.0041768 1.0058734 ## [1107] 1.0035350 1.0100406 1.0142164 1.0100497 1.0058233 1.0081484 1.0078002 ## [1114] 1.0142041 1.0069639 1.0073027 1.0137456 1.0132929 1.0104569 1.0109615 ## [1121] 1.0208995 1.0250735 1.0232000 1.0207126 1.0150926 1.0151053 1.0065024 ## [1128] 1.0091543 1.0061788 1.0072091 1.0041855 0.9973197 0.9970789 0.9986591 ## [1135] 1.0000015 0.9999881 0.9996030 1.0003984 1.0066467 1.0202177 1.0146234 ## [1142] 1.0289462 1.0210104 1.0291259 1.0152057 1.0107054 1.0114679 1.0028669 ## [1149] 1.0146576 1.0139600 1.0146620 1.0084333 1.0094910 1.0058826 1.0107211 ## [1156] 1.0036507 1.0079949 1.0077820 1.0006913 1.0021208 1.0000765 1.0019932 ## [1163] 1.0013721 1.0042568 1.0028252 0.9990946 1.0068074 1.0058818 1.0026606 ## [1170] 1.0013866 1.0023280 1.0042852 1.0070374 1.0045257 1.0003642 1.0025843 ## [1177] 1.0012878 1.0087018 1.0068735 1.0301547 1.0244383 1.0271763 1.0209514 ## [1184] 1.0246950 1.0335452 1.0428710 1.0359315 1.0399583 1.0422785 1.0525117 ## [1191] 1.0528560 1.0517930 1.0748263 1.0901181 1.0802320 1.0822756 1.0760489 ## [1198] 1.0675220 1.0736628 1.0687617 1.0768986 1.0683866 1.0561288 1.0610504 ## [1205] 1.0702635 1.0575191 1.0783128 1.0653537 1.0669697 1.0522965 1.0525902 ## [1212] 1.0531603 1.0431732 1.0373555 1.0447341 1.0232960 1.0160157 1.0049670 ## [1219] 1.0069839 1.0128089 1.0105958 1.0130063 1.0091465 1.0147042 1.0084594 ## [1226] 1.0142864 1.0196101 1.0252442 1.0063909 1.0065459 1.0038364 1.0014492 ## [1233] 1.0052279 1.0074165 1.0021169 1.0121685 1.0215987 1.0417103 1.0222426 ## [1240] 1.0328004 1.0176843 1.0081060 1.0002476 0.9998125 1.0040913 1.0151187 ## [1247] 1.0196038 1.0163858 1.0162379 1.0230286 1.0397711 1.0571276 1.0615074 ## [1254] 1.0511096 1.0406125 1.0587680 1.0456557 1.0519647 1.0388051 1.0305327 ## [1261] 1.0337479 1.0427278 1.0373852 1.0272337 1.0421199 1.0348837 1.0134220 ## [1268] 1.0143910 1.0108552 1.0069290 1.0170064 1.0180898 1.0250738 1.0244185 ## [1275] 1.0335119 1.0428104 1.0375288 1.0241971 1.0249235 1.0296429 1.0333879 ## [1282] 1.0524508 1.0287360 1.0267355 1.0186781 1.0156195 1.0176046 1.0235651 ## [1289] 1.0255783 1.0268602 1.0387355 1.0375290 1.0374039 1.0156087 1.0260445 ## [1296] 1.0440561 1.0472686 1.0409866 1.0494863 1.0552183 1.0295093 1.0235747 ## [1303] 1.0316372 1.0398092 1.0277397 1.0366173 1.0399206 1.0505498 1.0505354 ## [1310] 1.0231705 1.0279609 1.0408531 1.0481134 1.0352164 1.0265440 1.0368631 ## [1317] 1.0275208 1.0298337 1.0541787 1.0425602 1.0246430 1.0331014 1.0541599 ## [1324] 1.0430581 1.0415641 1.0363139 1.0440058 1.0463759 1.0270658 1.0211031 ## [1331] 1.0297284 1.0312761 1.0207089 1.0386388 1.0304763 1.0310275 1.0190168 ## [1338] 1.0170615 1.0305011 1.0326462 1.0280833 1.0367414 1.0241119 1.0389539 ## [1345] 1.0428926 1.0338663 1.0387997 1.0314505 1.0316412 1.0591119 1.0565085 ## [1352] 1.0655194 1.0662668 1.0500047 1.0525496 1.0626293 1.0553302 1.0521990 ## [1359] 1.0608070 1.0406838 1.0513366 1.0772339 1.1011411 1.1043428 1.1198700 ## [1366] 1.1245727 1.1162479 1.0917292 1.0886413 1.0402639 1.0056041 1.0081544 ## [1373] 1.0055950 1.0084610 1.0223585 1.0241668 1.0206284 1.0338030 1.0542355 ## [1380] 1.0495783 1.0599556 1.0553176 1.0704088 1.0613507 1.0765089 1.0760391 ## [1387] 1.0530020 1.0541359 1.0577929 1.0723551 1.0604215 1.0826172 1.0509797 ## [1394] 1.0502989 1.0536147 1.0570162 1.0720514 1.0760787 1.0805962 1.0546349 ## [1401] 1.0638714 1.0618101 1.0855562 1.0789916 1.0976731 1.0885384 1.0645001 ## [1408] 1.0329661 1.0416936 1.0254973 1.0279859 1.0147721 1.0440571 1.0692548 ## [1415] 1.0595093 1.0632863 1.0375232 1.0336484 1.0403449 1.0380611 1.0310961 ## [1422] 1.0375629 1.0339210 1.0123704 1.0159247 1.0119241 1.0213535 1.0192451 ## [1429] 1.0225596 1.0221631 1.0242955 1.0237550 1.0076895 1.0152258 1.0219191 ## [1436] 1.0185015 1.0185601 1.0120336 1.0120573 1.0129132 1.0171382 1.0247252 ## [1443] 1.0227517 1.0218722 1.0241930 1.0241023 1.0224949 1.0188597 1.0152929 ## [1450] 1.0108755 1.0158282 1.0153184 1.0278986 1.0335054 1.0189118 1.0216729 ## [1457] 1.0132555 1.0256879 1.0193767 1.0338238 1.0331623 1.0311919 1.0208044 ## [1464] 1.0181193 1.0181943 1.0096366 1.0113160 1.0074678 1.0040292 1.0114841 ## [1471] 1.0154072 1.0116428 1.0121810 1.0084209 1.0024953 1.0053792 1.0044868 ## [1478] 1.0061153 1.0115674 1.0077229 1.0060241 1.0044306 1.0182948 1.0201747 ## [1485] 1.0143774 1.0274217 1.0276946 1.0271920 1.0313688 1.0241680 1.0376641 ## [1492] 1.0335565 1.0403999 1.0342521 1.0252517 1.0164073 1.0294744 1.0286548 ## [1499] 1.0246086 1.0476741 1.0725873 1.0941640 1.0417349 1.0272140 1.0337478 ## [1506] 1.0224268 1.0084819 1.0165358 1.0117918 1.0130135 1.0139998 1.0220171 ## [1513] 1.0117930 1.0131028 1.0086078 1.0092125 1.0036981 1.0033246 1.0042009 ## [1520] 1.0067913 1.0102898 1.0119297 1.0128957 1.0180129 1.0228962 1.0272785 ## [1527] 1.0244763 1.0165326 1.0199880 1.0157726 1.0257601 1.0185735 1.0149514 ## [1534] 1.0140282 1.0145104 1.0046388 1.0077739 1.0069670 1.0245806 1.0115810 ## [1541] 1.0182225 1.0272782 1.0297159 1.0274229 1.0595689 1.0687228 1.0739774 ## [1548] 1.0729047 1.0530987 1.0356456 1.0347657 1.0509329 1.0332013 1.0389624 ## [1555] 1.0250612 1.0148143 1.0173199 1.0219845 1.0205430 1.0271189 1.0303202 ## [1562] 1.0163351 1.0183460 1.0168387 1.0264625 1.0380250 1.0165181 1.0166050 ## [1569] 1.0163493 1.0137271 1.0253963 1.0432056 1.0415883 1.0356546 1.0208515 ## [1576] 1.0230462 1.0380957 1.0311389 1.0245283 1.0124095 1.0193367 1.0196370 ## [1583] 1.0123492 1.0161890 1.0294797 1.0287406 1.0527480 1.0355271 1.0278174 ## [1590] 1.0193965 1.0174329 1.0263953 1.0401514 1.0586289 1.0529082 1.0612372 ## [1597] 1.0516081 1.0535490 1.0559506 1.0404321 1.0227261 1.0184573 1.0134050 ## [1604] 1.0177445 1.0081122 1.0144600 1.0130376 1.0160692 1.0214669 1.0132699 ## [1611] 1.0016088 0.9921320 1.0033283 1.0158060 1.0332072 1.0485173 1.0461176 ## [1618] 1.0397710 1.0350166 1.0140865 1.0111303 1.0046167 1.0028478 1.0125940 ## [1625] 1.0103416 1.0043494 1.0032242 1.0042762 0.9967927 0.9989186 0.9986768 ## [1632] 0.9986875 1.0002176 1.0023934 1.0061821 1.0115353 1.0121429 1.0165794 ## [1639] 1.0097136 1.0226218 1.0150167 1.0060419 1.0291688 1.0082333 1.0008128 ## [1646] 0.9992924 1.0218070 1.0424334 1.0454756 1.0352545 1.0469363 1.0820850 ## [1653] 1.0622202 1.0551218 1.0587881 1.0509672 1.0466953 1.0422250 1.0384709 ## [1660] 1.0330073 1.0279534 1.0179241 1.0127336 1.0059724 1.0051696 1.0028003 ## [1667] 1.0031811 1.0052171 1.0164931 1.0136340 1.0228598 1.0196355 1.0222364 ## [1674] 1.0308805 1.0560902 1.0535845 1.0595391 1.0911517 1.0687287 1.0672978 ## [1681] 1.0596484 1.0655634 1.0599007 1.0603649 1.0609138 1.0688428 1.0583710 ## [1688] 1.0593796 1.0486068 1.0336817 1.0417418 1.0517023 1.0404150 1.0437767 ## [1695] 1.0322430 1.0464871 1.0370812 1.0378105 1.0414022 1.0498121 1.0526388 ## [1702] 1.0398218 1.0521424 1.0521804 1.0761649 1.0728463 1.0761958 1.0591514 ## [1709] 1.0316252 1.0248109 1.0349353 1.0189857 1.0291591 1.0262322 1.0205585 ## [1716] 1.0309385 1.0164015 1.0208220 1.0183367 1.0156748 1.0139451 1.0166633 ## [1723] 1.0144786 1.0084249 1.0243626 1.0193523 1.0200216 1.0118016 1.0102974 ## [1730] 1.0123918 1.0169913 1.0170493 1.0122976 1.0124265 1.0081066 1.0079335 ## [1737] 1.0120797 1.0059616 1.0187830 1.0272996 1.0246632 1.0225078 1.0303737 ## [1744] 1.0326685 1.0274107 1.0333224 1.0269046 1.0295791 1.0188533 1.0256387 ## [1751] 1.0150162 1.0148500 1.0084826 1.0036766 1.0049694 1.0098855 1.0126021 ## [1758] 1.0104432 1.0083058 1.0033639 1.0022767 1.0053756 1.0045205 1.0166573 ## [1765] 1.0155885 1.0126164 1.0064415 1.0026477 1.0138634 1.0136237 1.0220362 ## [1772] 1.0282947 1.0200832 1.0290214 1.0106160 1.0269693 1.0423506 1.0684829 ## [1779] 1.0577817 1.0786022 1.0449160 1.0311601 1.0258434 1.0221236 1.0133927 ## [1786] 1.0124512 1.0211491 1.0221830 1.0214946 1.0304352 1.0196068 1.0340976 ## [1793] 1.0304705 1.0208807 1.0204019 1.0234921 1.0303580 1.0218168 1.0199082 ## [1800] 1.0322905 1.0527752 1.0371362 1.0365233 1.0387765 1.0434034 1.0364551 ## [1807] 1.0435576 1.0460926 1.0279951 1.0332586 1.0249754 1.0215610 1.0133433 ## [1814] 1.0091169 1.0073282 1.0019064 1.0062358 1.0122391 1.0126505 1.0148063 ## [1821] 1.0309796 1.0236384 1.0269869 1.0264564 1.0275989 1.0223493 1.0212676 ## [1828] 1.0130415 1.0016968 1.0005573 1.0030972 1.0036349 1.0030781 1.0009360 ## [1835] 1.0007202 1.0083140 1.0027610 1.0155434 1.0398945 1.0454447 1.0425240 ## [1842] 1.0449245 1.0393623 1.0343934 1.0296272 1.0451664 1.0465384 1.0278859 ## [1849] 1.0216679 1.0361006 1.0398764 1.0286293 1.0520371 1.0654144 1.0541372 ## [1856] 1.0484441 1.0553315 1.0873534 1.0662555 1.0574873 1.0473390 1.0392644 ## [1863] 1.0606268 1.0400117 1.0183265 1.0224700 1.0199188 1.0222688 1.0077350 ## [1870] 1.0156060 1.0195302 1.0197037 1.0193519 1.0326831 1.0388996 1.0288136 ## [1877] 1.0204036 1.0070373 1.0064186 1.0139920 1.0116878 1.0029385 1.0052307 ## [1884] 1.0059962 1.0067537 1.0119307 1.0184129 1.0164106 1.0175203 1.0179551 ## [1891] 1.0119622 1.0168937 1.0244200 1.0184931 1.0254367 1.0164007 1.0190966 ## [1898] 1.0286315 1.0204841 1.0251313 1.0224417 1.0212823 1.0376852 1.0394120 ## [1905] 1.0182900 1.0185101 1.0081679 1.0220810 1.0315531 1.0370215 1.0669832 ## [1912] 1.0532836 1.0666129 1.0695295 1.0792180 1.0623029 1.0499212 1.0481816 ## [1919] 1.0230212 1.0481085 1.0535348 1.0734309 1.0683064 1.0866247 1.0558187 ## [1926] 1.0495196 1.0602196 1.0335769 1.0346248 1.0243201 1.0151876 1.0086638 ## [1933] 1.0010820 1.0025613 1.0045216 1.0114537 1.0163795 1.0257376 1.0274077 ## [1940] 1.0290541 1.0249971 1.0272627 1.0279110 1.0196626 1.0298860 1.0412620 ## [1947] 1.0388480 1.0579935 1.0416968 1.0271604 1.0445272 1.0487768 1.0696937 ## [1954] 1.0594657 1.0657471 1.0891152 1.0844976 1.0945189 1.0618866 1.0392610 ## [1961] 1.0485568 1.0454606 1.0339765 1.0299410 1.0387928 1.0322615 1.0206576 ## [1968] 1.0117474 1.0088446 1.0089163 1.0138771 1.0310560 1.0298109 1.0439614 ## [1975] 1.0528040 1.0361240 1.0260367 1.0203335 1.0150052 1.0154761 1.0129618 ## [1982] 1.0228519 1.0220488 1.0235934 1.0129757 1.0024247 1.0060637 1.0197558 ## [1989] 1.0271540 1.0229853 1.0176453 1.0299825 1.0370293 1.0398339 1.0387137 ## [1996] 1.0489976 1.0511679 1.0543874 1.0402658 1.0354422 ``` ] --- * Plot the distribution 1/2 .center[ ![](practical6_files/figure-html/unnamed-chunk-4-1.svg)<!-- --> ] --- * Plot the distribution 2/2 .center[ ![](practical6_files/figure-html/unnamed-chunk-5-1.svg)<!-- --> ] --- * Get the probability that this quantity is strictly positive ```r mean(stupid > 0) ``` ``` ## [1] 1 ```