#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Tue Jan 23 13:51:20 2024

@author: 
"""

#Modules



#  uniforme
#tracer de la densité
    

D=rd.random(10000) 
#simulation d'un échantillonn de 10000 valeurs suivant une loi uniforme sur  [0,1[
plt.hist(D,color='goldenrod',density=True,bins=15)
#affichage d'un histogramme à 15 barres




def unif_densite(x):
    '''densité de la loi uniforme'''
    if x<0:
        return 0
    elif 0<x<1:
        return 1
    else:
        return 0

#tracer de la courbe eprésentative 
debut=-1
fin=2
nbpas=1000
X=[debut + k*(fin-debut)/nbpas for k in range(nbpas)]
Y=[unif_densite(x) for x in X]
plt.plot(X,Y)

plt.show()





































#Mystères

M1=[0.6805984038808668,
 1.7694687420372812,
 0.406327988458816,
 2.030035765415309,
 3.092610984554871,
 4.96844833178657,
 0.03115182669314743,
 4.872051652842015,
 0.5023233467618223,
 1.671392802614042,
 1.1534303180949854,
 1.222921816142357,
 1.866110049092276,
 3.4627703947522237,
 0.26649903755239834,
 0.3294287296200227,
 0.4978824177938912,
 2.006088339699347,
 1.6500309610484085,
 0.5495617273695781,
 4.14866397501777,
 1.669840518100518,
 6.788733489079358,
 3.9356000677144327,
 0.29920949170454136,
 3.572510132355267,
 4.05091210948051,
 1.1015067897322988,
 1.5035694996828166,
 5.960808903318538,
 3.840082533551513,
 2.462887209855124,
 0.12789724767373187,
 13.127147237898846,
 0.9597287610791138,
 0.6222565314959508,
 2.7292995858357827,
 0.8881428757420461,
 2.2003603838710166,
 6.330847981089025,
 0.8409207305866425,
 2.968421263523638,
 0.8122850762596011,
 2.0955532149939664,
 4.191009382974578,
 1.232229660151056,
 3.86668812729083,
 1.6802904640434217,
 3.116572279154222,
 6.628643001085273,
 4.791608805653201,
 5.262562645276452,
 2.94156204129114,
 0.9135803123661577,
 0.42662445872301763,
 1.6768520286847028,
 3.2256230261488055,
 0.8698230709291283,
 1.5738277147495925,
 2.288696922623777,
 0.6673099651513456,
 0.5568891897249113,
 0.963009312013725,
 3.3378564471424683,
 2.7442930103412553,
 0.4399958780010707,
 0.500237340703011,
 1.5924940378493346,
 2.8232927177759923,
 0.2292332976724572,
 0.43946934273960603,
 1.4847891060919358,
 1.6063379933679656,
 5.0863575565286085,
 2.648463395775345,
 8.154181983795684,
 3.9333301102081784,
 0.3675591996543474,
 0.6599902351566053,
 0.40875802395474536,
 4.9702478538452635,
 0.8833396906834693,
 0.6544478992302726,
 3.0686379308843255,
 0.7108690847823262,
 0.6000397064223096,
 0.6319708967533132,
 1.011559929010646,
 5.82823736551346,
 1.1459686391541768,
 0.30356632904953035,
 3.5268237823609856,
 3.017554474691992,
 2.561669557115857,
 0.36585782658768795,
 0.37088526092658197,
 0.419812933125791,
 3.5308222673727094,
 1.8184194060743002,
 2.7709121440477924,
 0.22143702380776756,
 4.260215830247005,
 5.037168574920946,
 3.9355330095183803,
 4.142301661603978,
 2.0173631390129376,
 0.7000419044315804,
 6.790282958869598,
 3.0724028429175707,
 0.2773731453651759,
 4.673962932374086,
 1.5593557825496696,
 0.6077662612697758,
 0.41955830007534456,
 0.9386158200053107,
 2.7284383212092873,
 4.769723466308163,
 1.8584633069475827,
 3.1124285623015235,
 4.016166141840517,
 1.1939152238645947,
 0.5815275181640129,
 5.3920460067554306,
 0.9195791975290816,
 0.8062431010357839,
 2.140593883369058,
 4.795438629099396,
 2.5760366704931483,
 0.216733815433051,
 3.285754220637583,
 1.366789541893052,
 1.6128921908606506,
 2.0905860430592784,
 2.232046596463755,
 2.9166869420699695,
 2.278044265605958,
 4.776693687320839,
 2.8981132058434267,
 0.3820219461598515,
 3.981322488289384,
 0.07832433684517875,
 5.014111006082591,
 5.236783373491192,
 3.402994875810174,
 1.2706982723114817,
 0.4831332115414484,
 3.163255144830337,
 1.7188308017762515,
 0.17366748908313875,
 0.11723976574322927]


M2=[-0.6702974065550215,
 0.24122199406978445,
 0.19772086197594896,
 -0.9163918068668773,
 1.0280463715126313,
 0.7957923585867613,
 0.8460146152359864,
 1.5081233900009787,
 0.44198681078289265,
 0.586736059620908,
 1.8944595143130727,
 0.042912301422440284,
 0.4687384995929983,
 0.688010053487121,
 1.1837679339497327,
 -1.054651318932312,
 -0.15196295003449065,
 0.631891703566777,
 -1.8180786381925849,
 1.4644327241999722,
 0.2361673345475077,
 -1.4099686768802824,
 0.7351022682925876,
 0.6463843285971596,
 0.2120319912063898,
 -0.8792618601327216,
 -1.0414969348492134,
 0.6060382882859222,
 0.22009486920747745,
 -1.0421864927678741,
 -0.9845925550064406,
 0.7990143193901469,
 0.30536802021998155,
 -0.36022872531044253,
 0.8091510355627639,
 -0.6821709021176434,
 -0.6843108461633663,
 -0.24976401486288244,
 -0.7921636624631503,
 -0.012856606180942773,
 -0.3822453163511697,
 0.06441308715651442,
 -0.13764351513260195,
 1.4554163690316086,
 -0.011285694501043105,
 0.4763878179794343,
 0.14700365507360974,
 0.07098233083784306,
 -1.3288197501749472,
 -0.7315584547039099,
 -0.15095066115214595,
 -0.28405060242372987,
 -2.261383641642718,
 -1.3063431309019047,
 0.696641594421094,
 -2.480817342526476,
 -0.4970132048871244,
 1.8436066555670212,
 0.6482183028716864,
 -2.0294630824696482,
 0.7951724651856963,
 1.7197078145060862,
 0.5422754478962725,
 -0.793405307654248,
 0.8391734632592969,
 -0.42436605412373396,
 -1.5900201096794748,
 -0.4689331484626432,
 -0.6135748198071378,
 0.9148072504738006,
 0.7337962335693428,
 -0.26727249938839864,
 2.1579132706089386,
 1.1333626052833237,
 0.4130571874138933,
 -0.4037581987608753,
 0.6511401021549187,
 -0.23404012011543637,
 -0.2849145511396549,
 -0.16544471844154868,
 0.01572942793055676,
 -0.5730041925305195,
 -0.22830080269230493,
 0.37522591549741635,
 1.7089590992078185,
 -1.0292747518935812,
 -1.749951719349441,
 0.48154566947377897,
 1.4639224157168276,
 -1.0247833735502196,
 2.2329705477526187,
 -1.2163713654968924,
 -0.32694029857035506,
 0.15933123500614546,
 -0.0401800984724817,
 0.8558464114918537,
 0.6691702813397303,
 -0.48672523103611454,
 -0.5664639873815891,
 3.1094781321619025,
 -0.24893913245719743,
 -0.532882731319475,
 0.9101257401751915,
 -1.1247867731222754,
 -0.7381986222204969,
 1.4481195045532833,
 -1.2299939009943026,
 -1.4630577925424546,
 0.17707348477387638,
 0.6837242727379272,
 -0.37242356835820456,
 -1.613089571245663,
 0.6306930903150052,
 -0.4466084711672842,
 0.09514825443831829,
 0.581262651237078,
 -0.1212986809469609,
 -0.19806765213046937,
 -3.519302108587796,
 -0.5042793562051385,
 0.1027427405059276,
 0.8661178268163751,
 0.46214458972306255,
 0.6739145191935758,
 0.9172724303265852,
 -0.07014321253529612,
 -0.4363055470152552,
 -0.09550894133309867,
 1.7175856623453079,
 0.4944268241929968,
 0.11859742378042641,
 -1.3505833705874466,
 -1.259385459189167,
 0.7861407332229775,
 1.186192935792371,
 1.0962461752201829,
 1.5069836014899727,
 -1.088063491417866,
 0.3821415706316987,
 -1.344390400739769,
 -0.19191790055402827,
 -0.9026393809249454,
 1.9606145016302006,
 1.2132340398722914,
 0.11440605457213618,
 0.07612717132700281,
 2.2534774792450936,
 -1.0600794890850729,
 -1.0125105604266922,
 0.6949093219171316]


M3=[0.23386934279312602,
 1.1743406817487696,
 0.24223708306825506,
 0.7628812869652648,
 0.11817270756215018,
 0.7514066511111082,
 0.6823411220987534,
 0.8770479699824217,
 1.3451641508280512,
 0.28850823997518626,
 0.3004879259666021,
 0.48560804955382436,
 0.09233889850628313,
 0.6597705256548743,
 0.35004858445767467,
 0.953128114050266,
 0.30266669022151604,
 1.032447161612686,
 0.5445130035314549,
 0.053217141327800324,
 0.32822183512971254,
 0.09024007535879475,
 0.07098008524387099,
 0.181885006306558,
 1.7337173583384078,
 0.4437674095406489,
 0.350152581300726,
 0.03856933751643796,
 0.4335396840425824,
 0.14640386715621695,
 0.1660784070147832,
 0.14658175509770818,
 0.09969594449043913,
 0.3172662017707841,
 1.8960171788388755,
 1.7415570626606596,
 0.1586327999957619,
 0.04877165340438731,
 0.15304076401130653,
 0.08595685045732195,
 0.5729205125278237,
 0.24902342207462982,
 0.3885550764012405,
 0.022770837101756362,
 0.08845949281612939,
 0.05898335370469194,
 0.036616098408850654,
 0.9261619346236605,
 0.06656571210115786,
 0.33850141605971124,
 0.4908888114950373,
 0.088330408379372,
 0.0030005357666804946,
 0.502609059098516,
 0.029077556682105776,
 0.2709179016740087,
 0.10439436900222648,
 0.2514418810781065,
 0.04466414349939923,
 0.03593832688541524,
 0.10122639785741748,
 0.5573735722536401,
 0.1260129266565922,
 0.05336008940662623,
 1.0447626284154579,
 0.039049225326407665,
 0.3550012153053957,
 0.5064986896831646,
 1.4796718051570976,
 0.2709436021104568,
 0.2436430506048349,
 1.3056273641393703,
 0.7820462351962935,
 0.5179219548248831,
 0.7356630114027284,
 1.652339144897236,
 0.7712180196207078,
 0.9093903118653489,
 0.12656411832887665,
 1.3625842739315184,
 0.20512060261001236,
 0.5328675713144764,
 0.3498964639647657,
 0.005834223796339346,
 1.002732869278861,
 0.2366269445682602,
 1.2396746820439646,
 0.1253015046586467,
 1.1763359104584945,
 0.01679323000417451,
 0.0656937460936012,
 1.309111816920921,
 0.27432056243040026,
 0.6862185137621641,
 0.12053070523177674,
 0.6364637075324476,
 0.463836270316149,
 0.5787002094004502,
 0.45329206535062533,
 0.0693879150805931,
 0.2615954186405528,
 1.1291096865180972,
 0.6189592013044777,
 1.3079989188531902,
 0.5405106312555618,
 0.12571717688994294,
 0.06585194531686955,
 0.6792038091409834,
 0.49913799040246054,
 0.2738671086317936,
 0.6800832633254171,
 0.5974776526381924,
 0.8446831579733053,
 0.20877415887179598,
 0.007075114378939903,
 0.2796900773228659,
 0.08569442054812275,
 0.3766470733021137,
 0.8991487896234591,
 0.1014234069651036,
 1.0995442575213037,
 0.2674600855752897,
 0.03941469757168665,
 0.08517452468786531,
 0.01305620188793805,
 2.589764433988887,
 0.6482227336221211,
 0.5008537533597215,
 0.2238955076665919,
 0.7264075321151819,
 1.4838666258456121,
 0.34635970059053073,
 1.170962081277152,
 0.2363186986614544,
 0.023575452234353166,
 0.07480249733045168,
 0.355574669801175,
 0.039739200751532804,
 0.6449286678334755,
 0.2579967369113884,
 1.1451621819890792,
 0.6255762657522568,
 0.14279454929427457,
 0.9263080001012617,
 0.2402907840567872,
 0.15402645123967962,
 0.08354172403524714,
 0.005355145306690493,
 0.8464861077827524,
 0.11649521639333701]

M4=[-0.6860922884412888,
 -1.8401070728907571,
 -0.8434251336155273,
 -4.451072137300642,
 -0.6537557777371372,
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 2.4007205883016702,
 0.0949183864504819,
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 0.32115949629736473,
 -1.7786591303206434]