512mb-bot/resources/default.json

{"discuss":{"Markov":{"probability":1,"occurences":1}},"Many":{"uses":{"probability":1,"occurences":1}},"future":{"actions":{"probability":0.5,"occurences":2},"states":{"probability":0.5,"occurences":2}},"Markov":{"chains;":{"probability":0.0625,"occurences":16},"property.":{"probability":0.25,"occurences":64},"chains":{"probability":0.25,"occurences":64},"chain":{"probability":0.3125,"occurences":80},"property,":{"probability":0.0625,"occurences":16},"chain,":{"probability":0.0625,"occurences":16}},"conditional":{"probability":{"probability":0.5,"occurences":2},"independence.":{"probability":0.5,"occurences":2}},"1.":{"In":{"probability":1,"occurences":1}},"arise":{"broadly":{"probability":1,"occurences":1}},"of)":{"future":{"probability":1,"occurences":1}},"(communication)":{"theory,":{"probability":1,"occurences":1}},"particular":{"state":{"probability":1,"occurences":1}},"all":{"that":{"probability":0.125,"occurences":2},"possible":{"probability":0.125,"occurences":2},"scores,":{"probability":0.125,"occurences":2},"is,":{"probability":0.125,"occurences":2},"color,":{"probability":0.125,"occurences":2},"is":{"probability":0.25,"occurences":4},"later":{"probability":0.125,"occurences":2}},"asks":{"what":{"probability":0.5,"occurences":2},"once":{"probability":0.5,"occurences":2}},"scores,":{"or":{"probability":1,"occurences":1}},"ball":{"later":{"probability":0.16666666666667,"occurences":5},"scores,":{"probability":0.16666666666667,"occurences":5},"is,":{"probability":0.16666666666667,"occurences":5},"is":{"probability":0.33333333333333,"occurences":10},"color,":{"probability":0.16666666666667,"occurences":5}},"stochastic":{"process":{"probability":0.6,"occurences":15},"properties":{"probability":0.2,"occurences":5},"process,":{"probability":0.2,"occurences":5}},"are":{"not":{"probability":0.16666666666667,"occurences":6},"focused":{"probability":0.16666666666667,"occurences":6},"widely":{"probability":0.16666666666667,"occurences":6},"fixed.":{"probability":0.16666666666667,"occurences":6},"many":{"probability":0.16666666666667,"occurences":6},"removed,":{"probability":0.16666666666667,"occurences":6}},"what":{"the":{"probability":1,"occurences":4}},"at":{"do":{"probability":0.076923076923077,"occurences":2},"is,":{"probability":0.15384615384615,"occurences":4},"led":{"probability":0.076923076923077,"occurences":2},"no":{"probability":0.076923076923077,"occurences":2},"the":{"probability":0.15384615384615,"occurences":4},"is":{"probability":0.076923076923077,"occurences":2},"its":{"probability":0.076923076923077,"occurences":2},"random":{"probability":0.076923076923077,"occurences":2},"experiences":{"probability":0.076923076923077,"occurences":2},"a":{"probability":0.076923076923077,"occurences":2},"of":{"probability":0.076923076923077,"occurences":2}},"X_1,":{"\\,":{"probability":1,"occurences":1}},"different.":{"A":{"probability":1,"occurences":1}},"therefore":{"time-inhomogeneous":{"probability":1,"occurences":1}},"change.":[],"sum":{"of":{"probability":1,"occurences":1}},"current":{"state":{"probability":0.5,"occurences":2},"state.":{"probability":0.5,"occurences":2}},"mathematical":{"system":{"probability":1,"occurences":1}},"a":{"labeled":{"probability":0.052631578947368,"occurences":19},"certain":{"probability":0.10526315789474,"occurences":38},"prolific":{"probability":0.052631578947368,"occurences":19},"general":{"probability":0.052631578947368,"occurences":19},"process":{"probability":0.052631578947368,"occurences":19},"finite":{"probability":0.052631578947368,"occurences":19},"Markov":{"probability":0.15789473684211,"occurences":57},"sequence":{"probability":0.052631578947368,"occurences":19},"way,":{"probability":0.052631578947368,"occurences":19},"stochastic":{"probability":0.15789473684211,"occurences":57},"mathematical":{"probability":0.052631578947368,"occurences":19},"ball":{"probability":0.052631578947368,"occurences":19},"bag":{"probability":0.052631578947368,"occurences":19},"time-homogeneous":{"probability":0.052631578947368,"occurences":19}},"same":{"question":{"probability":1,"occurences":1}},"matrix":{"methods.":{"probability":1,"occurences":1}},"necessary":{"to":{"probability":1,"occurences":1}},"any":{"vertex's":{"probability":0.14285714285714,"occurences":4},"size":{"probability":0.14285714285714,"occurences":4},"\"everyday\"":{"probability":0.14285714285714,"occurences":4},"uses":{"probability":0.14285714285714,"occurences":4},"state":{"probability":0.14285714285714,"occurences":4},"particular":{"probability":0.14285714285714,"occurences":4},"common":{"probability":0.14285714285714,"occurences":4}},"It":{"could":{"probability":1,"occurences":1}},"its":{"present":{"probability":1,"occurences":1}},"transitioning":{"to":{"probability":1,"occurences":1}},"finance.":{"While":{"probability":1,"occurences":1}},"machines,":{"and":{"probability":1,"occurences":1}},"begins":{"to":{"probability":1,"occurences":1}},"focused":{"on":{"probability":1,"occurences":1}},"color":{"ball":{"probability":0.5,"occurences":8},"for":{"probability":0.5,"occurences":8}},"be":{"modeled":{"probability":0.2,"occurences":5},"drastically":{"probability":0.2,"occurences":5},"\"memory-less.\"":{"probability":0.2,"occurences":5},"visualized":{"probability":0.2,"occurences":5},"anything:":{"probability":0.2,"occurences":5}},"important":{"precisely":{"probability":1,"occurences":1}},"led":{"the":{"probability":0.25,"occurences":1},"by":{"probability":0.25,"occurences":1},"up":{"probability":0.25,"occurences":1},"directed":{"probability":0.25,"occurences":1}},"sequence":{"X0, X1, X2, …X_0,":{"probability":1,"occurences":1}},"there":{"are":{"probability":1,"occurences":1}},"many":{"\"everyday\"":{"probability":0.5,"occurences":2},"common":{"probability":0.5,"occurences":2}},"That":{"is,":{"probability":1,"occurences":1}},"conditions,":{"baseball":{"probability":1,"occurences":1}},"drawn.":{"Once":{"probability":1,"occurences":1}},"also":{"ask":{"probability":1,"occurences":1}},"property.":{"While":{"probability":0.25,"occurences":4},"Depending":{"probability":0.25,"occurences":4},"Can":{"probability":0.25,"occurences":4},"A":{"probability":0.25,"occurences":4}},"replacement":{"each":{"probability":1,"occurences":1}},"state,":{"the":{"probability":1,"occurences":1}},"non-stationary":{"transition":{"probability":1,"occurences":1}},"number":{"of":{"probability":1,"occurences":1}},"bag":{"of":{"probability":1,"occurences":1}},"elapsed.":{"The":{"probability":1,"occurences":1}},"creates":{"a":{"probability":1,"occurences":1}},"rules.":{"The":{"probability":1,"occurences":1}},"weather":{"conditions,":{"probability":1,"occurences":1}},"\"memory-less.\"":{"That":{"probability":1,"occurences":1}},"game":{"theory,":{"probability":1,"occurences":1}},"than":{"the":{"probability":1,"occurences":1}},"that":{"no":{"probability":0.125,"occurences":8},"experiences":{"probability":0.125,"occurences":8},"do":{"probability":0.125,"occurences":8},"led":{"probability":0.125,"occurences":8},"of":{"probability":0.125,"occurences":8},"is,":{"probability":0.125,"occurences":8},"is":{"probability":0.125,"occurences":8},"a":{"probability":0.125,"occurences":8}},"cases":{"with":{"probability":1,"occurences":1}},"(steps":{"increase),":{"probability":1,"occurences":1}},"differs":{"from":{"probability":1,"occurences":1}},"process,":{"but":{"probability":0.5,"occurences":2},"however,":{"probability":0.5,"occurences":2}},"process":{"begins":{"probability":0.2,"occurences":5},"may":{"probability":0.2,"occurences":5},"in":{"probability":0.2,"occurences":5},"with":{"probability":0.2,"occurences":5},"arrived":{"probability":0.2,"occurences":5}},"again,":{"this":{"probability":1,"occurences":1}},"called":{"the":{"probability":1,"occurences":1}},"chains;":{"that":{"probability":1,"occurences":1}},"out":{"why?":{"probability":1,"occurences":1}},"chain,":{"in":{"probability":1,"occurences":1}},"question":{"asks":{"probability":1,"occurences":4}},"time-inhomogeneous":{"Markov":{"probability":1,"occurences":1}},"anything:":{"letters,":{"probability":1,"occurences":1}},"the":{"same":{"probability":0.03125,"occurences":31},"initial":{"probability":0.03125,"occurences":31},"Markov":{"probability":0.15625,"occurences":155},"rule":{"probability":0.03125,"occurences":31},"possible":{"probability":0.03125,"occurences":31},"one":{"probability":0.03125,"occurences":31},"language":{"probability":0.03125,"occurences":31},"current":{"probability":0.0625,"occurences":62},"next":{"probability":0.03125,"occurences":31},"probability":{"probability":0.25,"occurences":248},"steps":{"probability":0.03125,"occurences":31},"process":{"probability":0.03125,"occurences":31},"sum":{"probability":0.03125,"occurences":31},"theory":{"probability":0.03125,"occurences":31},"labels":{"probability":0.03125,"occurences":31},"random":{"probability":0.0625,"occurences":62},"previous":{"probability":0.03125,"occurences":31},"present":{"probability":0.03125,"occurences":31},"most":{"probability":0.03125,"occurences":31}},"rule":{"of":{"probability":1,"occurences":1}},"why?":{"In":{"probability":1,"occurences":1}},"by":{"finite":{"probability":1,"occurences":1}},"must":{"be":{"probability":1,"occurences":1}},"states":{"are":{"probability":1,"occurences":1}},"definition":{"is":{"probability":1,"occurences":1}},"matter":{"how":{"probability":1,"occurences":1}},"The":{"state":{"probability":0.5,"occurences":2},"defining":{"probability":0.5,"occurences":2}},"of":{"any":{"probability":0.08,"occurences":50},"their":{"probability":0.04,"occurences":25},"the":{"probability":0.2,"occurences":125},"state":{"probability":0.04,"occurences":25},"getting":{"probability":0.08,"occurences":50},"states.":{"probability":0.04,"occurences":25},"Markov":{"probability":0.08,"occurences":50},"all":{"probability":0.04,"occurences":25},"moving":{"probability":0.04,"occurences":25},"multi-colored":{"probability":0.04,"occurences":25},"conditional":{"probability":0.08,"occurences":50},"time.":{"probability":0.04,"occurences":25},"random":{"probability":0.04,"occurences":25},"transitioning":{"probability":0.04,"occurences":25},"a":{"probability":0.08,"occurences":50},"stochastic":{"probability":0.04,"occurences":25}},"visualized":{"with":{"probability":1,"occurences":1}},"other":{"words,":{"probability":0.5,"occurences":4},"according":{"probability":0.25,"occurences":2},"may":{"probability":0.25,"occurences":2}},"infinite)":{"number":{"probability":1,"occurences":1}},"broader":{"than":{"probability":1,"occurences":1}},"require":{"proficiency":{"probability":1,"occurences":1}},"variables,":{"a":{"probability":1,"occurences":1}},"their":{"usefulness":{"probability":1,"occurences":1}},"does":{"not":{"probability":0.5,"occurences":2},"satisfy":{"probability":0.5,"occurences":2}},"in":{"probabilistic":{"probability":0.071428571428571,"occurences":5},"color":{"probability":0.14285714285714,"occurences":10},"must":{"probability":0.071428571428571,"occurences":5},"is":{"probability":0.28571428571429,"occurences":20},"statistical":{"probability":0.071428571428571,"occurences":5},"economics,":{"probability":0.071428571428571,"occurences":5},"which":{"probability":0.071428571428571,"occurences":5},"that":{"probability":0.071428571428571,"occurences":5},"mathematics.":{"probability":0.071428571428571,"occurences":5},"for":{"probability":0.071428571428571,"occurences":5}},"usefulness":{"in":{"probability":1,"occurences":1}},"not":{"dependent":{"probability":0.33333333333333,"occurences":3},"satisfy":{"probability":0.66666666666667,"occurences":6}},"can":{"be":{"probability":1,"occurences":1}},"time.":{"Such":{"probability":1,"occurences":1}},"baseball":{"scores,":{"probability":1,"occurences":1}},"you":{"figure":{"probability":1,"occurences":1}},"probabilistic":{"rules.":{"probability":1,"occurences":1}},"broadly":{"in":{"probability":1,"occurences":1}},"space,":{"the":{"probability":0.5,"occurences":2},"or":{"probability":0.5,"occurences":2}},"when":{"selecting":{"probability":1,"occurences":1}},"labels":{"of":{"probability":1,"occurences":1}},"language":{"of":{"probability":1,"occurences":1}},"In":{"the":{"probability":0.2,"occurences":5},"such":{"probability":0.2,"occurences":5},"probability":{"probability":0.2,"occurences":5},"other":{"probability":0.4,"occurences":10}},"dependent":{"solely":{"probability":0.33333333333333,"occurences":2},"upon":{"probability":0.33333333333333,"occurences":2},"of":{"probability":0.33333333333333,"occurences":2}},"upon":{"the":{"probability":0.5,"occurences":2},"which":{"probability":0.5,"occurences":2}},"Can":{"you":{"probability":1,"occurences":1}},"words,":{"the":{"probability":0.5,"occurences":2},"knowledge":{"probability":0.5,"occurences":2}},"possible":{"states,":{"probability":0.33333333333333,"occurences":3},"future":{"probability":0.33333333333333,"occurences":3},"to":{"probability":0.33333333333333,"occurences":3}},"size":{"of":{"probability":1,"occurences":1}},"or":{"for":{"probability":0.2,"occurences":4},"countably":{"probability":0.1,"occurences":2},"set":{"probability":0.1,"occurences":2},"stock":{"probability":0.1,"occurences":2},"ball":{"probability":0.3,"occurences":6},"which":{"probability":0.1,"occurences":2},"non-stationary":{"probability":0.1,"occurences":2}},"finite":{"state":{"probability":0.5,"occurences":2},"(or":{"probability":0.5,"occurences":2}},"theory,":{"queueing":{"probability":0.33333333333333,"occurences":3},"genetics,":{"probability":0.33333333333333,"occurences":3},"the":{"probability":0.33333333333333,"occurences":3}},"genetics,":{"and":{"probability":1,"occurences":1}},"multi-colored":{"balls.":{"probability":1,"occurences":1}},"ask":{"what":{"probability":1,"occurences":1}},"with":{"any":{"probability":0.16666666666667,"occurences":6},"common":{"probability":0.16666666666667,"occurences":6},"a":{"probability":0.33333333333333,"occurences":12},"color":{"probability":0.33333333333333,"occurences":12}},"balls":{"are":{"probability":1,"occurences":1}},"Such":{"a":{"probability":1,"occurences":1}},"allows":{"replacement":{"probability":0.5,"occurences":2},"for":{"probability":0.5,"occurences":2}},"walks":{"provide":{"probability":1,"occurences":1}},"system":{"that":{"probability":1,"occurences":1}},"increase),":{"the":{"probability":1,"occurences":1}},"this":{"creates":{"probability":1,"occurences":1}},"set":{"of":{"probability":1,"occurences":1}},"experiences":{"transitions":{"probability":1,"occurences":1}},"above,":{"as":{"probability":1,"occurences":1}},"according":{"to":{"probability":1,"occurences":1}},"\\,":{"X_2,":{"probability":0.33333333333333,"occurences":3},"X_1,":{"probability":0.33333333333333,"occurences":3},"\\dotsX0​,X1​,X2​,…":{"probability":0.33333333333333,"occurences":3}},"distribution":{"of":{"probability":1,"occurences":1}},"letters,":{"numbers,":{"probability":1,"occurences":1}},"(the":{"probability":{"probability":1,"occurences":1}},"however,":{"does":{"probability":1,"occurences":1}},"widely":{"employed":{"probability":1,"occurences":1}},"from":{"one":{"probability":0.5,"occurences":8},"a":{"probability":0.5,"occurences":8}},"such":{"a":{"probability":1,"occurences":1}},"for":{"the":{"probability":0.4,"occurences":10},"ball":{"probability":0.2,"occurences":5},"which":{"probability":0.2,"occurences":5},"non-stationary":{"probability":0.2,"occurences":5}},"one":{"state":{"probability":0.66666666666667,"occurences":6},"explored":{"probability":0.33333333333333,"occurences":3}},"uses":{"of":{"probability":1,"occurences":1}},"another":{"according":{"probability":0.5,"occurences":2},"may":{"probability":0.5,"occurences":2}},"They":{"arise":{"probability":1,"occurences":1}},"economics,":{"game":{"probability":1,"occurences":1}},"fixed.":{"In":{"probability":1,"occurences":1}},"and":{"are":{"probability":0.1,"occurences":10},"it":{"probability":0.1,"occurences":10},"information-theoretical":{"probability":0.1,"occurences":10},"so":{"probability":0.1,"occurences":10},"therefore":{"probability":0.1,"occurences":10},"random":{"probability":0.2,"occurences":20},"time":{"probability":0.1,"occurences":10},"finance.":{"probability":0.1,"occurences":10},"most":{"probability":0.1,"occurences":10}},"explored":{"above,":{"probability":1,"occurences":1}},"no":{"matter":{"probability":1,"occurences":1}},"edges":{"is":{"probability":1,"occurences":1}},"knowledge":{"of":{"probability":1,"occurences":1}},"time":{"a":{"probability":0.33333333333333,"occurences":3},"goes":{"probability":0.33333333333333,"occurences":3},"elapsed.":{"probability":0.33333333333333,"occurences":3}},"time-homogeneous":{"Markov":{"probability":1,"occurences":1}},"labeled":{"directed":{"probability":1,"occurences":1}},"do":{"not":{"probability":1,"occurences":1}},"drastically":{"different.":{"probability":1,"occurences":1}},"goes":{"on":{"probability":1,"occurences":1}},"vertex's":{"outgoing":{"probability":1,"occurences":1}},"balls.":{"It":{"probability":1,"occurences":1}},"getting":{"a":{"probability":1,"occurences":4}},"moving":{"from":{"probability":1,"occurences":1}},"how":{"the":{"probability":1,"occurences":1}},"mathematics.":{"They":{"probability":1,"occurences":1}},"variables":{"satisfying":{"probability":1,"occurences":1}},"to":{"any":{"probability":0.125,"occurences":8},"exist":{"probability":0.125,"occurences":8},"determine":{"probability":0.125,"occurences":8},"discuss":{"probability":0.125,"occurences":8},"another":{"probability":0.25,"occurences":16},"the":{"probability":0.125,"occurences":8},"certain":{"probability":0.125,"occurences":8}},"variable,":{"and":{"probability":1,"occurences":1}},"X0, X1, X2, …X_0,":{"\\,":{"probability":1,"occurences":1}},"present":{"state,":{"probability":0.5,"occurences":2},"state.":{"probability":0.5,"occurences":2}},"variant":{"of":{"probability":1,"occurences":1}},"independence.":{"In":{"probability":1,"occurences":1}},"independent":{"of":{"probability":1,"occurences":1}},"theory":{"and":{"probability":0.5,"occurences":2},"of":{"probability":0.5,"occurences":2}},"exist":{"with":{"probability":1,"occurences":1}},"\"everyday\"":{"processes":{"probability":1,"occurences":1}},"prolific":{"example":{"probability":1,"occurences":1}},"characteristic":{"of":{"probability":1,"occurences":1}},"as":{"it":{"probability":0.5,"occurences":2},"time":{"probability":0.5,"occurences":2}},"certain":{"probabilistic":{"probability":0.33333333333333,"occurences":3},"color":{"probability":0.66666666666667,"occurences":6}},"immediate":{"example":{"probability":1,"occurences":1}},"applications":{"are":{"probability":1,"occurences":1}},"may":{"be":{"probability":0.75,"occurences":12},"change.":{"probability":0.25,"occurences":4}},"once":{"again":{"probability":1,"occurences":1}},"defining":{"characteristic":{"probability":1,"occurences":1}},"next":{"ball":{"probability":1,"occurences":1}},"is":{"that":{"probability":0.10526315789474,"occurences":32},"drawn.":{"probability":0.052631578947368,"occurences":16},"possible":{"probability":0.052631578947368,"occurences":16},"process,":{"probability":0.052631578947368,"occurences":16},"is":{"probability":0.052631578947368,"occurences":16},"important":{"probability":0.052631578947368,"occurences":16},"dependent":{"probability":0.052631578947368,"occurences":16},"all":{"probability":0.052631578947368,"occurences":16},"necessary":{"probability":0.052631578947368,"occurences":16},"broader":{"probability":0.052631578947368,"occurences":16},"independent":{"probability":0.052631578947368,"occurences":16},"definition":{"probability":0.052631578947368,"occurences":16},"1.":{"probability":0.052631578947368,"occurences":16},"when":{"probability":0.052631578947368,"occurences":16},"a":{"probability":0.15789473684211,"occurences":48},"creates":{"probability":0.052631578947368,"occurences":16}},"later":{"may":{"probability":1,"occurences":1}},"proficiency":{"with":{"probability":1,"occurences":1}},"X_2,":{"\\,":{"probability":1,"occurences":1}},"information-theoretical":{"contexts":{"probability":1,"occurences":1}},"so":{"ask":{"probability":0.33333333333333,"occurences":2},"on.":{"probability":0.33333333333333,"occurences":2},"many":{"probability":0.33333333333333,"occurences":2}},"because":{"so":{"probability":1,"occurences":1}},"general":{"stochastic":{"probability":1,"occurences":1}},"on.":{"In":{"probability":1,"occurences":1}},"could":{"also":{"probability":1,"occurences":1}},"determine":{"the":{"probability":1,"occurences":1}},"on":{"matrix":{"probability":0.071428571428571,"occurences":3},"cases":{"probability":0.071428571428571,"occurences":3},"is":{"probability":0.14285714285714,"occurences":6},"the":{"probability":0.14285714285714,"occurences":6},"examples":{"probability":0.071428571428571,"occurences":3},"probability":{"probability":0.071428571428571,"occurences":3},"probabilities":{"probability":0.071428571428571,"occurences":3},"which":{"probability":0.071428571428571,"occurences":3},"of":{"probability":0.071428571428571,"occurences":3},"(steps":{"probability":0.071428571428571,"occurences":3},"asks":{"probability":0.14285714285714,"occurences":6}},"A":{"Markov":{"probability":0.5,"occurences":8},"variant":{"probability":0.25,"occurences":4},"common":{"probability":0.25,"occurences":4}},"countably":{"infinite)":{"probability":1,"occurences":1}},"Once":{"again,":{"probability":1,"occurences":1}},"queueing":{"(communication)":{"probability":1,"occurences":1}},"modeled":{"by":{"probability":1,"occurences":1}},"performances.":{"Markov":{"probability":1,"occurences":1}},"methods.":{"A":{"probability":1,"occurences":1}},"again":{"for":{"probability":1,"occurences":1}},"example":{"of":{"probability":0.5,"occurences":2},"is":{"probability":0.5,"occurences":2}},"satisfy":{"the":{"probability":1,"occurences":16}},"actions":{"are":{"probability":1,"occurences":1}},"figure":{"out":{"probability":1,"occurences":1}},"(or":{"countably":{"probability":1,"occurences":1}},"arrived":{"at":{"probability":1,"occurences":1}},"up":{"to":{"probability":1,"occurences":1}},"steps":{"increase),":{"probability":0.5,"occurences":1},"that":{"probability":0.5,"occurences":1}},"processes":{"satisfy":{"probability":1,"occurences":1}},"state.":{"This":{"probability":1,"occurences":4}},"This":{"process,":{"probability":0.33333333333333,"occurences":3},"is":{"probability":0.33333333333333,"occurences":3},"definition":{"probability":0.33333333333333,"occurences":3}},"way,":{"a":{"probability":1,"occurences":1}},"probability":{"theory,":{"probability":0.090909090909091,"occurences":11},"of)":{"probability":0.090909090909091,"occurences":11},"of":{"probability":0.54545454545455,"occurences":66},"question":{"probability":0.090909090909091,"occurences":11},"and":{"probability":0.090909090909091,"occurences":11},"distribution":{"probability":0.090909090909091,"occurences":11}},"\\dotsX0​,X1​,X2​,…":{"of":{"probability":1,"occurences":1}},"statistical":{"and":{"probability":1,"occurences":1}},"property,":{"there":{"probability":1,"occurences":1}},"previous":{"state":{"probability":1,"occurences":1}},"solely":{"on":{"probability":1,"occurences":1}},"random":{"variable,":{"probability":0.16666666666667,"occurences":6},"walks":{"probability":0.16666666666667,"occurences":6},"from":{"probability":0.16666666666667,"occurences":6},"variable.":{"probability":0.16666666666667,"occurences":6},"variables":{"probability":0.16666666666667,"occurences":6},"variables,":{"probability":0.16666666666667,"occurences":6}},"but":{"it":{"probability":1,"occurences":4}},"common":{"matrix":{"probability":0.33333333333333,"occurences":3},"examples":{"probability":0.33333333333333,"occurences":3},"probability":{"probability":0.33333333333333,"occurences":3}},"is,":{"and":{"probability":0.33333333333333,"occurences":3},"as":{"probability":0.33333333333333,"occurences":3},"(the":{"probability":0.33333333333333,"occurences":3}},"selecting":{"uniformly":{"probability":1,"occurences":1}},"uniformly":{"at":{"probability":1,"occurences":1}},"numbers,":{"weather":{"probability":1,"occurences":1}},"initial":{"theory":{"probability":1,"occurences":1}},"chains":{"with":{"probability":0.25,"occurences":4},"require":{"probability":0.25,"occurences":4},"is":{"probability":0.25,"occurences":4},"may":{"probability":0.25,"occurences":4}},"removed,":{"the":{"probability":1,"occurences":1}},"outgoing":{"edges":{"probability":1,"occurences":1}},"properties":{"that":{"probability":1,"occurences":1}},"Depending":{"upon":{"probability":1,"occurences":1}},"examples":{"of":{"probability":1,"occurences":1}},"provide":{"a":{"probability":1,"occurences":1}},"state":{"space,":{"probability":0.22222222222222,"occurences":18},"transition":{"probability":0.11111111111111,"occurences":9},"and":{"probability":0.11111111111111,"occurences":9},"to":{"probability":0.22222222222222,"occurences":18},"is":{"probability":0.22222222222222,"occurences":18},"machines,":{"probability":0.11111111111111,"occurences":9}},"states.":{"Many":{"probability":1,"occurences":1}},"color,":{"but":{"probability":1,"occurences":1}},"chain":{"is":{"probability":0.8,"occurences":20},"must":{"probability":0.2,"occurences":5}},"variable.":{"This":{"probability":1,"occurences":1}},"precisely":{"because":{"probability":1,"occurences":1}},"each":{"time":{"probability":1,"occurences":1}},"contexts":{"and":{"probability":1,"occurences":1}},"transition":{"is":{"probability":0.5,"occurences":2},"probabilities":{"probability":0.5,"occurences":2}},"stock":{"performances.":{"probability":1,"occurences":1}},"directed":{"graph,":{"probability":1,"occurences":1}},"graph,":{"for":{"probability":1,"occurences":1}},"transitions":{"from":{"probability":1,"occurences":1}},"states,":{"can":{"probability":1,"occurences":1}},"employed":{"in":{"probability":1,"occurences":1}},"While":{"the":{"probability":0.5,"occurences":2},"it":{"probability":0.5,"occurences":2}},"probabilities":{"and":{"probability":1,"occurences":1}},"which":{"balls":{"probability":0.33333333333333,"occurences":3},"the":{"probability":0.66666666666667,"occurences":6}},"it":{"differs":{"probability":0.2,"occurences":5},"allows":{"probability":0.4,"occurences":10},"is":{"probability":0.2,"occurences":5},"does":{"probability":0.2,"occurences":5}},"satisfying":{"the":{"probability":1,"occurences":1}},"most":{"immediate":{"probability":0.5,"occurences":2},"applications":{"probability":0.5,"occurences":2}}}