Problem 1
x=1.1
a=2.2
b=3.3
# part a
z <- x^(a^b)
print(z)
## [1] 3.61714
# part b
z <- (x^a)^b
print(z)
## [1] 1.997611
# part c
z <- 3*x^3 + 2*x^2 +1
print(z)
## [1] 7.413
# part d
help(floor)
(z %% 1)
## [1] 0.413
floor((z %% 1)*10)
## [1] 4
# Another way to do part d (Lauren Ash)
round((z-round(z,0)),1)*10
## [1] 4
Problem 2
# part a
z <- c(rep(1:8), rep(7:1))
print(z)
## [1] 1 2 3 4 5 6 7 8 7 6 5 4 3 2 1
# part b
z <- rep(1:5, c(1:5))
print(z)
## [1] 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5
# part c
z <- rep(5:1, c(1:5))
print(z)
## [1] 5 4 4 3 3 3 2 2 2 2 1 1 1 1 1
Problem 3
xy <- runif(2)
xy
## [1] 0.8489840 0.9047966
theta <- atan(xy[2]/xy[1])
theta
## [1] 0.8172116
r<-sqrt((xy[1]^2) + (xy[2]^2))
r
## [1] 1.240738
p <- c(r, theta)
p
## [1] 1.2407380 0.8172116
Problem 4
queue <- c("sheep", "fox", "owl", "ant")
queue
## [1] "sheep" "fox" "owl" "ant"
# part a
queue[5] <- "serpent"
queue
## [1] "sheep" "fox" "owl" "ant" "serpent"
# part b
queue <- queue[-1]
queue
## [1] "fox" "owl" "ant" "serpent"
# part c
queue<- c("donkey", queue)
queue
## [1] "donkey" "fox" "owl" "ant" "serpent"
# part d
queue <- queue[-5]
queue
## [1] "donkey" "fox" "owl" "ant"
# part e
queue <- queue[-3]
queue
## [1] "donkey" "fox" "ant"
# part f
queue <- c(queue[1:2], "aphid", queue[3])
queue
## [1] "donkey" "fox" "aphid" "ant"
# part g
grep("aphid", queue)
## [1] 3
Problem 5
z <- (1:100)
z<- z[-which(z%%2==0)]
z<- z[-which(z%%3==0)]
z<- z[-which(z%%7==0)]
z
## [1] 1 5 11 13 17 19 23 25 29 31 37 41 43 47 53 55 59 61 65 67 71 73 79
## [24] 83 85 89 95 97
# A one-line way to do this
z <- z[z%%2 !=0 & z%%3 !=0 & z%%7 !=0]
print(z)
## [1] 1 5 11 13 17 19 23 25 29 31 37 41 43 47 53 55 59 61 65 67 71 73 79
## [24] 83 85 89 95 97
Problem 6
z<-runif(1000)
print(z)
## [1] 0.3574420759 0.5360117822 0.6995494682 0.7607985002 0.6929017557
## [6] 0.1232803876 0.8852719176 0.5486810382 0.1242462560 0.3287743914
## [11] 0.5328353292 0.7298125771 0.5360599752 0.2075480411 0.7381139384
## [16] 0.1882987516 0.3704332297 0.9214162068 0.0923180643 0.9576113359
## [21] 0.9654115951 0.8399150972 0.0232993262 0.6872144933 0.5394299505
## [26] 0.2518786874 0.6256745111 0.5897385962 0.5279350448 0.5923007424
## [31] 0.7398082570 0.1203011677 0.8165586868 0.4377447378 0.9690882820
## [36] 0.6879680904 0.8283052847 0.8281818500 0.7538924171 0.9847247428
## [41] 0.2880487810 0.0343604253 0.4919424967 0.6109023143 0.7579670995
## [46] 0.1364725963 0.4993160674 0.4228605560 0.4029665207 0.9690984227
## [51] 0.9968087252 0.3379973888 0.7561173043 0.2662261981 0.2599717572
## [56] 0.2456434467 0.3570770761 0.8995117603 0.1143297616 0.5864960586
## [61] 0.4004455088 0.2643750096 0.6941923050 0.6396834811 0.4167564770
## [66] 0.2338470053 0.7791817209 0.9094978720 0.1952099747 0.3303528177
## [71] 0.2942265291 0.0337450202 0.8096710246 0.7772402796 0.5978347922
## [76] 0.1906283649 0.6239505990 0.0336054547 0.7064802290 0.2844451114
## [81] 0.5830584657 0.7041500651 0.3871966605 0.0234188726 0.2323191904
## [86] 0.7664110456 0.3734981588 0.9947574446 0.9163979096 0.5936419235
## [91] 0.0374339016 0.8045384032 0.8609525899 0.6714322108 0.5776073574
## [96] 0.4557783129 0.9528172603 0.7688886670 0.2511990906 0.2219607958
## [101] 0.6612383742 0.1684009694 0.1586612798 0.2705177271 0.9352332640
## [106] 0.4849760449 0.7969219452 0.5377626615 0.9676284648 0.7311362778
## [111] 0.7265234396 0.4736738801 0.4245081232 0.9638123380 0.8760777514
## [116] 0.8940799828 0.0621462734 0.0774437990 0.1791415366 0.0259075018
## [121] 0.8968479394 0.2164067968 0.6379081730 0.7378649525 0.0731633217
## [126] 0.8484989861 0.8919395329 0.6844504902 0.0239276513 0.7047700102
## [131] 0.1834869143 0.8490186525 0.3921304266 0.4948674163 0.0283345650
## [136] 0.8225445612 0.9574834704 0.8478749965 0.9052539426 0.3346822499
## [141] 0.7784015425 0.5917308978 0.6729968023 0.2818232977 0.1718979864
## [146] 0.7828523272 0.6395432455 0.2438093689 0.3331996435 0.7344466420
## [151] 0.0312959985 0.5146549270 0.8165979658 0.0379223956 0.6915451013
## [156] 0.8059269600 0.4719033625 0.9433771379 0.4128719822 0.0947991633
## [161] 0.4285639187 0.3240405512 0.2536156902 0.8441839896 0.3350932964
## [166] 0.9178050978 0.7134416453 0.6474252592 0.5837488796 0.1117722488
## [171] 0.6674706354 0.7542798005 0.1567436263 0.1879214759 0.0356566920
## [176] 0.3485793513 0.5104084120 0.9362654169 0.6755070786 0.8883365206
## [181] 0.6281685338 0.1593009231 0.2601902494 0.1403266506 0.0312181639
## [186] 0.8681194985 0.4512036087 0.8087344577 0.2670348657 0.6955166114
## [191] 0.3471441010 0.4909475513 0.1017677060 0.7524344861 0.5789109704
## [196] 0.9325079655 0.1581348137 0.4898628043 0.0143816336 0.6737885878
## [201] 0.3107629537 0.6241130177 0.8354744455 0.5129115633 0.8604095103
## [206] 0.4058360476 0.3477494249 0.1321610676 0.4191944029 0.7848884971
## [211] 0.2449283930 0.5241489694 0.6933893787 0.6097411530 0.8203905171
## [216] 0.5166164837 0.2805709511 0.4829286924 0.6757722334 0.4226424741
## [221] 0.5225904104 0.1981315596 0.4638635858 0.9507307529 0.7022200343
## [226] 0.2509842995 0.5840437852 0.3293993948 0.4192140149 0.0972628286
## [231] 0.7905704463 0.7687317240 0.9614161891 0.3411916597 0.3934846078
## [236] 0.9198825201 0.8430639666 0.0007515815 0.9256580283 0.2312722844
## [241] 0.2578172344 0.9234891380 0.3539715097 0.5236589646 0.6396829393
## [246] 0.3302655786 0.3370861185 0.4354782682 0.9078352044 0.2936647551
## [251] 0.1202230095 0.6546056969 0.7994098165 0.1472204675 0.8655071277
## [256] 0.1420960443 0.8947852498 0.5088761740 0.0001340776 0.5846369541
## [261] 0.5588260985 0.4384029703 0.6513208058 0.0483703180 0.9772924036
## [266] 0.8704077683 0.3502773163 0.6103718146 0.1004722491 0.4993350038
## [271] 0.3620128981 0.5740368739 0.5798804457 0.2513002427 0.4687058011
## [276] 0.8842379921 0.2370114082 0.9456949132 0.6866803684 0.7880634216
## [281] 0.5917790397 0.0201491052 0.6988104053 0.4887353524 0.4961030658
## [286] 0.9308905113 0.1704831980 0.6736520384 0.8817769212 0.8293311724
## [291] 0.9080403354 0.2093988280 0.6031391509 0.8539190679 0.7735642428
## [296] 0.4592870842 0.1995147194 0.3793512254 0.8178129052 0.7491426356
## [301] 0.0437254938 0.2836626524 0.8798370033 0.2901434740 0.9359143751
## [306] 0.1180232086 0.8492461143 0.5869676005 0.0711199502 0.6170010692
## [311] 0.4245219498 0.8917583288 0.8196023151 0.4160964084 0.5694907079
## [316] 0.7204688382 0.9812885297 0.0251365998 0.9904162844 0.1364489540
## [321] 0.3826168298 0.1197195277 0.6655386807 0.9737078322 0.4131729398
## [326] 0.4901267402 0.7074885222 0.1120531331 0.6481008942 0.7080731560
## [331] 0.2846532508 0.9695881677 0.2651783763 0.0686944528 0.2824842974
## [336] 0.9685072037 0.2364128707 0.1644284662 0.3078810058 0.5807051843
## [341] 0.8633829374 0.1051579770 0.9526203556 0.7470184278 0.7686271826
## [346] 0.5667489651 0.7640680433 0.4603326942 0.6669666294 0.6586601366
## [351] 0.5596310254 0.8888969030 0.2540970314 0.7111336358 0.0322705705
## [356] 0.2133335322 0.7580074081 0.6037690844 0.0238803071 0.0510956536
## [361] 0.1486448520 0.7347149707 0.4776133732 0.2101920529 0.3977334280
## [366] 0.4138404205 0.0500986916 0.0984893220 0.2277386577 0.6452911415
## [371] 0.9628725280 0.3375579577 0.1623673183 0.7952687165 0.3975820525
## [376] 0.6839648199 0.8639565702 0.2188256097 0.0122283266 0.7669045038
## [381] 0.1607945412 0.9978135501 0.8232910007 0.5779134955 0.8224468715
## [386] 0.2663812884 0.2401314597 0.5653732342 0.4160192183 0.2129015462
## [391] 0.7291487593 0.4468755038 0.8765270899 0.1226113967 0.1718985704
## [396] 0.6934311923 0.5265218548 0.7099846583 0.3145335615 0.8765441899
## [401] 0.6299893737 0.8407194470 0.5666904857 0.1133535316 0.3130222156
## [406] 0.4693262305 0.2318193985 0.0959024669 0.3453639550 0.8576297250
## [411] 0.4505335374 0.8093827791 0.8855038772 0.3276042426 0.2862936947
## [416] 0.8189950187 0.9037355434 0.4874773780 0.8181718364 0.2243649068
## [421] 0.0065550271 0.2289962317 0.5922498379 0.1424696746 0.5442526196
## [426] 0.8035502648 0.9100129241 0.5230496046 0.6264667164 0.4093541345
## [431] 0.1488120656 0.6518532932 0.9354611158 0.8656425471 0.4973969327
## [436] 0.6501528709 0.2483025212 0.8335647269 0.1975822600 0.1639961998
## [441] 0.0996870925 0.8795716569 0.0527650679 0.4034255231 0.8111118777
## [446] 0.9157636904 0.1736531095 0.1055941919 0.6531482770 0.9806608409
## [451] 0.2399396652 0.6236763822 0.5831062330 0.8976018708 0.3242561128
## [456] 0.1938481692 0.3403513322 0.6043408753 0.2476488433 0.7185563552
## [461] 0.7197451175 0.0867918602 0.1407864592 0.2706802492 0.2897167099
## [466] 0.1967266970 0.6940480464 0.7752868857 0.2492034780 0.4395193018
## [471] 0.0003201773 0.1526446883 0.0719491283 0.0543387765 0.2907156411
## [476] 0.9097976128 0.8230898536 0.8557880060 0.5078627968 0.3996333913
## [481] 0.7057928143 0.0484652948 0.9923556878 0.6211726554 0.1495858396
## [486] 0.5946593368 0.0268301745 0.6460881899 0.7059287413 0.0775423881
## [491] 0.3508729492 0.3094640560 0.1865448931 0.3617661810 0.8179194489
## [496] 0.7814635595 0.3050263075 0.0584313646 0.7421287994 0.1865492943
## [501] 0.4429573044 0.8920284109 0.3064045820 0.4591039766 0.2462938481
## [506] 0.0331895016 0.4471406417 0.4360656007 0.1078416714 0.3986151887
## [511] 0.1640502661 0.7822919122 0.2469909515 0.6915885194 0.3732479801
## [516] 0.3216711313 0.1286141113 0.6321869148 0.2693495855 0.1207158775
## [521] 0.5266302202 0.9487264541 0.0090053137 0.6405254896 0.3721288459
## [526] 0.4968287465 0.3195680289 0.3560998519 0.6810977969 0.0627826748
## [531] 0.2553128363 0.9588358928 0.7665064449 0.9342831632 0.1731637558
## [536] 0.2515617132 0.8984630872 0.6847702025 0.9477282627 0.4957898934
## [541] 0.0713604905 0.3260733061 0.2894228825 0.8971785463 0.1829925335
## [546] 0.2237157391 0.3066737805 0.4486502511 0.0942803679 0.0596616992
## [551] 0.3085167154 0.4688548162 0.0281339036 0.5092443044 0.5443053474
## [556] 0.9202250028 0.7632999164 0.1446804493 0.1455869265 0.3730432298
## [561] 0.1160804455 0.4032170898 0.8609191023 0.0842036533 0.6477947957
## [566] 0.4049241673 0.9334059092 0.6958017836 0.0854883837 0.7735159113
## [571] 0.3674818210 0.2201609747 0.5875707488 0.3576635763 0.8901868456
## [576] 0.4062447452 0.7204776499 0.9023049560 0.0606136988 0.3859908073
## [581] 0.4887798603 0.5951332392 0.1366367314 0.5611730227 0.8641499116
## [586] 0.1102401812 0.0273755372 0.6105261408 0.5440444173 0.3455320755
## [591] 0.5031604234 0.6010714308 0.2472302895 0.7595320684 0.4679426246
## [596] 0.5502554367 0.4070083522 0.5895863140 0.4911153161 0.1482081262
## [601] 0.6207438097 0.1971802542 0.2869837119 0.9059671951 0.5831661471
## [606] 0.6377971382 0.9610706817 0.5779849479 0.1909364345 0.8121160220
## [611] 0.2578191932 0.2627176482 0.4065552049 0.6629104542 0.5918696001
## [616] 0.9720526580 0.4230666223 0.2025590816 0.8097581582 0.6683830998
## [621] 0.8424397560 0.4217194596 0.4626854630 0.9779452835 0.8860965767
## [626] 0.9986769194 0.1159964339 0.1267205239 0.2293584498 0.5493903328
## [631] 0.7339019321 0.4972258254 0.3326575889 0.6729857423 0.7018920728
## [636] 0.9111638214 0.0573570076 0.7142646573 0.3715467195 0.4122075664
## [641] 0.8389101948 0.3043530844 0.2887715243 0.9955873936 0.4671150732
## [646] 0.6934667081 0.3812330361 0.2573478625 0.5895296463 0.7153074844
## [651] 0.7393687053 0.6458602403 0.1504994673 0.1362924248 0.9835173313
## [656] 0.2335767958 0.1574173318 0.5482788994 0.5672878833 0.4245449791
## [661] 0.3340853797 0.5169875259 0.6237642635 0.2510073045 0.1493114599
## [666] 0.1306740975 0.3623488180 0.3292291574 0.8567454503 0.8690246637
## [671] 0.9848762611 0.8650819554 0.0094701643 0.3865367814 0.4943456782
## [676] 0.2089954645 0.5870606105 0.2486810142 0.5945490187 0.7913154212
## [681] 0.9838849269 0.9428677342 0.8785592341 0.7959287984 0.0592016384
## [686] 0.1164473540 0.0384400431 0.9662055769 0.8205240911 0.2709378528
## [691] 0.6875646811 0.6391757566 0.8290732063 0.2274912144 0.9093883664
## [696] 0.2873321008 0.2904265758 0.5896404400 0.2704386923 0.1031786711
## [701] 0.3507785227 0.6375796457 0.6435812879 0.7772156936 0.4688048735
## [706] 0.5141627090 0.1535804411 0.0795900517 0.7988155871 0.7305170533
## [711] 0.8398491009 0.2277773593 0.0447751512 0.4604958158 0.9080547944
## [716] 0.7975489262 0.5095076784 0.2541239085 0.1641966596 0.6164512017
## [721] 0.5080832362 0.9550614916 0.3620115533 0.9535073228 0.5217865210
## [726] 0.7568954802 0.1994712783 0.4664656788 0.8765949148 0.5364354895
## [731] 0.4088080679 0.8204201912 0.8706867311 0.2909021084 0.3931731989
## [736] 0.2733710678 0.4720498822 0.2524088351 0.2689848035 0.4123469519
## [741] 0.4485904316 0.2918955020 0.2857033999 0.3424081255 0.2505462759
## [746] 0.5840824421 0.2640289669 0.3405989239 0.4431428320 0.9937840421
## [751] 0.9783224687 0.0014948088 0.1338243601 0.1966178354 0.3696081520
## [756] 0.9794359505 0.1062091847 0.4223741542 0.6597778031 0.9639314667
## [761] 0.3234944348 0.5104472365 0.7560394141 0.4087428525 0.0662397952
## [766] 0.9472539355 0.8303819341 0.8403236773 0.0037204565 0.0670884142
## [771] 0.2624519505 0.4493961586 0.5306362845 0.0230717389 0.4381807207
## [776] 0.2334226058 0.4183274060 0.3666043854 0.4069380234 0.9395987804
## [781] 0.7981357896 0.0983997551 0.3977923971 0.8765366569 0.1586482369
## [786] 0.8343194525 0.0249136717 0.8322795432 0.9716534873 0.0937139571
## [791] 0.7673594719 0.7308431524 0.5712201339 0.4873002646 0.4205242549
## [796] 0.6475199196 0.2672492301 0.7204563362 0.8819131670 0.0071895835
## [801] 0.0212032660 0.7130106327 0.6269655370 0.1013423966 0.2335526510
## [806] 0.0805430561 0.4460668042 0.4673060412 0.9763115754 0.2043348891
## [811] 0.5165857726 0.1375546749 0.1985293666 0.6839866231 0.6462584746
## [816] 0.8205682198 0.1960225243 0.0780223261 0.7173083399 0.0183400062
## [821] 0.2105706241 0.1727750967 0.9123438811 0.1143879434 0.8074414362
## [826] 0.2031195925 0.4179222207 0.8495439021 0.6484971549 0.2018482380
## [831] 0.3843361083 0.8695833497 0.7659621516 0.9849387836 0.9196444040
## [836] 0.3555242396 0.9121230678 0.0882451579 0.9300900581 0.3204150484
## [841] 0.3827520423 0.3002590679 0.7318886530 0.7801559134 0.9625874292
## [846] 0.3718774801 0.9386136685 0.6250325465 0.9005251096 0.3404264485
## [851] 0.4919282354 0.6070530801 0.5167730744 0.5039946905 0.2294058590
## [856] 0.5313361229 0.3609114301 0.9772347789 0.8972897448 0.8180998974
## [861] 0.0822310606 0.9533794103 0.2602103292 0.7803587180 0.4957226918
## [866] 0.7042004711 0.6411139998 0.7879931482 0.8028936088 0.5128185940
## [871] 0.2286437615 0.9065743235 0.1681304288 0.9849277870 0.2814267247
## [876] 0.7202505665 0.2143899461 0.6826011057 0.3600227726 0.3134208270
## [881] 0.5618834367 0.5036285238 0.0337453519 0.3133761277 0.3420102221
## [886] 0.1171984335 0.1674957827 0.1073460761 0.8862272087 0.4249078776
## [891] 0.3674247107 0.9402775674 0.3044706765 0.1035425321 0.2702544720
## [896] 0.5258819887 0.1612997507 0.6324184800 0.7591224883 0.6219146824
## [901] 0.9754176685 0.5180830297 0.3240345700 0.9662264667 0.4662863605
## [906] 0.8769475555 0.8675877729 0.1917697357 0.8669390420 0.0748192940
## [911] 0.7520259100 0.3116401613 0.2866782434 0.4290549629 0.6486924822
## [916] 0.4910619787 0.7285338691 0.4547621168 0.1939501928 0.2401864203
## [921] 0.8895148500 0.1496099324 0.1006672964 0.5648754956 0.7500583758
## [926] 0.2639212271 0.1012555314 0.9271786690 0.5921528293 0.7359134376
## [931] 0.1340041999 0.3915381902 0.6782764459 0.1448350549 0.0423504906
## [936] 0.3080876165 0.3954759731 0.5873480381 0.6019993885 0.0996237970
## [941] 0.0250692812 0.3403704013 0.7296345062 0.0206271887 0.1729270970
## [946] 0.7271965474 0.7466572323 0.5701481341 0.9325219071 0.5094176205
## [951] 0.4288925673 0.6844098361 0.2085807964 0.3827569820 0.8535926642
## [956] 0.3572840958 0.8886930952 0.2769615690 0.3465789156 0.3697306805
## [961] 0.4326652354 0.1981355629 0.1747489476 0.2418430741 0.7703861119
## [966] 0.8044754961 0.4470498997 0.7014450566 0.8937212513 0.9681707711
## [971] 0.6495541378 0.4944245284 0.4917570762 0.4162112400 0.8132679113
## [976] 0.2724539463 0.1213936715 0.7302707513 0.4509900839 0.7895059972
## [981] 0.4102018657 0.7841339891 0.2973836020 0.3789696111 0.4640000579
## [986] 0.3424876742 0.2026607769 0.9939799160 0.4385255645 0.4572017186
## [991] 0.9752662824 0.3666460537 0.2929021891 0.5945406863 0.5545503527
## [996] 0.4589350817 0.5447492416 0.1693694773 0.9444206501 0.8767838706
# part a
a <- c((mean(z < 0.1)), (mean(z > 0.9)), (mean(z > 0.45 & z < 0.55)))
a
## [1] 0.084 0.098 0.096
# part b
z<-log10(z)
head(z)
## [1] -0.4467943 -0.2708257 -0.1551816 -0.1187304 -0.1593283 -0.9091060
b <- c((mean(z < 0.1)), (mean(z > 0.9)), (mean(z > 0.45 & z < 0.55)))
b
## [1] 1 0 0
z<-z^2
head(z)
## [1] 0.19962517 0.07334654 0.02408132 0.01409690 0.02538552 0.82647374
c <- c((mean(z < 0.1)), (mean(z > 0.9)), (mean(z > 0.45 & z < 0.55)))
c
## [1] 0.511 0.099 0.035
z<-(exp(1))^z
head(z)
## [1] 1.220945 1.076103 1.024374 1.014197 1.025710 2.285246
d <- c((mean(z < 0.1)), (mean(z > 0.9)), (mean(z > 0.45 & z < 0.55)))
d
## [1] 0 1 0
z<-sqrt(z)
head(z)
## [1] 1.104964 1.037354 1.012113 1.007073 1.012774 1.511703
e <- c((mean(z < 0.1)), (mean(z > 0.9)), (mean(z > 0.45 & z < 0.55)))
e
## [1] 0 1 0