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[{"key": "dc.contributor.advisor", "value": "Laitinen, Anni", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Naskali, Matias", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2021-05-04T06:03:42Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2021-05-04T06:03:42Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2021", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/75281", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4m\u00e4 tutkielma k\u00e4sittelee normaalijakaumaa ja siihen liittyv\u00e4\u00e4 todenn\u00e4k\u00f6isyysteoriaa. Lis\u00e4ksi osana tutkielmaa on laadittu lukion pitk\u00e4n matematiikan lis\u00e4oppimateriaaliksi tarkoitettu teht\u00e4v\u00e4paketti.\n\nJohdannossa k\u00e4sitell\u00e4\u00e4n normaalijakauman historiaa ja sivutaan normaalijakauman merkityst\u00e4 luonnontieteiss\u00e4. Lis\u00e4ksi johdannossa kuvaillaan lyhyesti tutkielman kappaleiden aiheita.\n\nKappaleissa 2-8 k\u00e4yd\u00e4\u00e4n l\u00e4pi normaalijakaumaan liittyv\u00e4\u00e4 todenn\u00e4k\u00f6isyysteoriaa. Teoriaosuuden p\u00e4\u00e4tulos on keskeinen raja-arvolause, joka todistetaan kappaleessa 8. Teoriaosuuden muut kappaleet k\u00e4sittelev\u00e4t keskeisen raja-arvolauseen ja sen todistuksen ymm\u00e4rt\u00e4misen kannalta t\u00e4rkeit\u00e4 todenn\u00e4k\u00f6isyysteorian kohtia. T\u00e4m\u00e4n lis\u00e4ksi kappaleessa 5 esitell\u00e4\u00e4n Monte Carlo -simulointiin liittyv\u00e4\u00e4 teoriaa. Simulointi on keskeinen havainnollistamisen keino tutkielman osana laadituissa teht\u00e4viss\u00e4.\n\nTutkielman viimeisess\u00e4 kappaleessa pohditaan sit\u00e4, miksi normaalijakauman teoreettista taustaa ei esitell\u00e4 lukiossa. Lis\u00e4ksi kappaleessa kuvaillaan, mitk\u00e4 ovat olleet keskeisimm\u00e4t ajatukset tutkielman liitteen\u00e4 olevan teht\u00e4v\u00e4paketin taustalla.\n\nTutkielman liitteen\u00e4 oleva teht\u00e4v\u00e4paketti pyrkii havainnollistamaan normaalijakauman teoreettista taustaa lukiotasolle soveltuvasti. Teht\u00e4v\u00e4paketti sis\u00e4lt\u00e4\u00e4 teht\u00e4v\u00e4t, teht\u00e4ville laaditut vastaukset sek\u00e4 teht\u00e4vien sis\u00e4lt\u00f6\u00e4 ja aiheita kuvailevan osion. Tutkielman lukeminen ei ole teht\u00e4v\u00e4paketin k\u00e4ytt\u00e4misen kannalta v\u00e4ltt\u00e4m\u00e4t\u00f6nt\u00e4.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2021-05-04T06:03:42Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2021-05-04T06:03:42Z (GMT). No. of bitstreams: 0\n Previous issue date: 2021", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "68", "language": "", "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "todenn\u00e4k\u00f6isyysavaruus", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "satunnaismuuttuja", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "keskeinen raja-arvolause", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Normaalijakauman teoreettinen tausta ja sen havainnollistuksia lukiotasolle", "language": "", "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-202105042595", "language": "", "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikan opettajankoulutus", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Teacher education programme in Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4041", "language": "", "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": 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