Dzidziso yeZvingangoitika muStatistics
Dzidziso yefungidziro yefungidziro inyaya inokosha yehuwandu hwezviverengero. Muchinyorwa chino, tichatsanangura zvakadzama dzidziso yefungidziro yefungidziro, kubva papfungwa dzayo dzepakutanga kusvika pakushandiswa kwayo muhuwandu hwezviverengero. Tichakurukurawo nhoroondo yayo, tsananguro yayo, misimboti yayo yekutanga, uye mienzaniso yakati wandei yekushandiswa kwayo muhupenyu hwezuva nezuva.
Nhoroondo yeDzidziso yeZvingangoitika
Kukura kwekutanga kwedzidziso yekufungidzira mukana kwakabva mukudiwa kwekunzwisisa nekuongorora mitambo yemhanza (kubhejera). Nhoroondo inotaura kuti mipiro mikuru yekutanga kudzidziso iyi yakabva kuvanyanzvi vemasvomhu vekuFrance Blaise Pascal naPierre de Fermat muzana remakore rechi17. Vakataura nezvedambudziko rakakonzereswa nemutambi wemitambo ainzi Antoine Gombaud, Chevalier de Méré. Hurukuro yavo yakaburitsa hwaro hwedzidziso yekufungidzira mukana, iyo yakazosimudzirwazve nevamwe nyanzvi dzemasvomhu vakaita saChristiaan Huygens, Jakob Bernoulli, naPierre-Simon Laplace.
Tsanangudzo yeMukana
Mikana yekuitika imhando yemuyero wekuti chiitiko chingaitika. Panyaya yemasvomhu, mukana wekuitika unoratidzwa senhamba iri pakati pa0 na1. Chiitiko chisingaitike chine mukana we0, nepo chiitiko chichaitika chine mukana we1.
Kune nzira dzakasiyana-siyana dzekutsanangura mukana:
1. Maitiro Ekare:
Mikana yechiitiko inhamba yehuwandu hwemhedzisiro inotsigira chiitiko ichocho nenhamba yemhedzisiro yese inogona kuitika munzvimbo yemuenzaniso.
\[
P(A) = \frac{|A|}{|S|}
\]
Apo \( |A| \) iri nhamba yemigumisiro inotsigira A, uye \( |S| \) iri nhamba yese yemigumisiro iri munzvimbo yemuenzaniso S.
2. Maitiro eKuwanda Kwezviitiko:
Mikana yekuti chiitiko chiitike ndiyo muganho wehuwandu hwechiitiko ichocho mumiedzo yakawanda.
\[
P(A) = \lim_{n \to \infty} \frac{n_A}{n}
\]
3. Maitiro Ekufunga Nezvemunhu:
Mikana ipfungwa yemunhu yekuti chiitiko chichaitika. Nzira iyi inowanzo shandiswa mumamiriro ezvinhu apo pasina ruzivo rwakakwana rwenhoroondo, uye kutonga kwemunhu pachake kwakakosha.
Dzidziso dzeBasic Axioms neTheorems dzeProbability Theory
Dzidziso yefungidziro yefungidziro yakavakirwa pazvirevo zvakakosha zvakatanga kugadzirwa naAndrey Kolmogorov muna 1933. Heano matatu maaxioms ekutanga:
1. Axiom yekusava nepfungwa dzakaipa:
Kune chero chiitiko A, mukana wekuti P(A) hausi wekuti uri negative.
\[
P(A) \geq 0
\]
2. Axiom Yese:
Mikana yekuti nzvimbo yemuenzaniso S isvike pa1.
\[
P(S) = 1
\]
3. Axiom yekuwedzera:
Pazviitiko zviviri zvisingabatanidzwi A na B (hapana zvinhu zvakafanana), mukana wekusanganiswa kwezviitiko zviviri izvi ndiwo huwandu hwemikana yechiitiko chimwe nechimwe.
\[
P(A \cup B) = P(A) + P(B)
\]
Zvichibva pamashoko aya, dzidziso dzinoverengeka dzinokosha dzinogona kuwanikwa:
- Dzidziso Inoenderana:
\[
P(A^c) = 1 – P(A)
\]
Apo \( A^c \) iri mukwanisi weA (zviitiko zvisina kubatanidzwa muA).
- Dzidziso yekuwedzera yeZviitiko Zviviri Zvisiri Zvega:
\[
P(A \cup B) = P(A) + P(B) – P(A \cup B)
\]
Apo \( A \cap B \) ndipo panosangana A naB (chiitiko chinosanganisirwa muzviitiko zvose zviri zviviri).
Zvimiro Zvisina Kurongeka uye Kugoverwa Kwemikana
Chinoshanduka-shanduka chinoshandiswa pakushandura chinhu chinobatanidza mhedzisiro yega yega iri munzvimbo yemuenzaniso nenhamba chaiyo. Zvinoshanduka-shanduka zvinogona kuiswa mumhando mbiri:
1. Zvikamu Zvisina Kurongwa Zvakasiyana:
Kutora kukosha kubva paseti ine finite kana kuti inoverengeka. Muenzaniso: huwandu hwemativi anoonekwa pakukanda dhayisi mbiri.
2. Zvishandiso Zvisingachinji Zvichienderera:
Inotora kukosha kweseti yenhamba chaidzo muchikamu. Muenzaniso: kukwirira kwemunhu.
Chinoshanduka-shanduka chega chega chine mukana wekugoverwa kwezvinogona kuitika unotsanangura mukana wechinhu chimwe nechimwe chinogoneka. Kune zvi-variable zvisina kurongeka zvakasiyana, kugoverwa uku kunonzi basa re-probability mass (PMF), nepo kune zvi-variable zvisina kurongeka zvinoenderera mberi, kunonzi basa re-probability density (PDF).
Basa reKuwanda Kwemukana (PMF):
\[
P(X = x_i) = p_i
\]
Basa reKuwanda Kwemukana (PDF):
\[
f(x) \geq 0 \quad \text{and} \quad \int_{-\infty}^{\infty} f(x) \, dx = 1
\]
Mamwe mashandisirwo anowanzo shandiswa ekuwedzera mikana ndeaya:
- Kugoverwa kweBinomial: Kunoshandiswa kutevedzera miedzo yeBernoulli yakadzokororwa nekubudirira kana kukundikana, senge kukanda mari.
- Kugoverwa kwakajairika kana kuti kweGaussian: Kunoshandiswa padata rakafanana uye rakaita sebhero, senge kureba kwehuwandu hwevanhu.
Mashandisirwo edzidziso yeProbability muStatistics
Dzidziso yefungidziro inokosha muhuwandu, kunyanya kana tichitarisa fungidziro yehuwandu, iyo inosanganisira kufungidzira kweparameter, kuyedza fungidziro, uye kufanotaura. Heano mamwe mashandisirwo akakosha:
1. Kufungidzira kweStatistical:
Mukufungidzira kwehuwandu hwevanhu, dzidziso yeprobability inoshandiswa kugadzira mhedziso pamusoro pehuwandu hwevanhu zvichibva pamuenzaniso wedata. Izvi zvinosanganisira kushandiswa kwefungidziro dzepoindi nedzepakati, pamwe nekuyedza fungidziro.
2. Muenzaniso weKudzoreredza:
Kudzoreredza (Regression) inzira inoshandiswa kutsanangura hukama huripo pakati pezvinhu zvinotsamira pazviri uye zvakazvimiririra. Mikana inoshandiswa kuona kuti modhi yacho inoenderana sei nedata uye kufanotaura.
3. Kuongorora Kusiyana (ANOVA):
Nzira iyi inoshandiswa kuenzanisa nzira dzemapoka akati wandei uye kuona kana musiyano wacho wakakosha muhuwandu hwemashoko. Mikana inoshandiswa kuverenga p-value, iyo inobatsira pakuita sarudzo.
Mikana muhupenyu hwezuva nezuva
Dzidziso yefungidziro haingoshandiswi muzvidzidzo zvedzidzo chete, asiwo ine mashandisirwo akawanda anoshanda muhupenyu hwezuva nezuva:
– Inishuwarenzi: Makambani einishuwarenzi anoshandisa mukana wekuverenga mari yeinishuwarenzi uye kugadzirisa njodzi dzeinishuwarenzi.
– Mitambo neMabheti: Mikana inoshandiswa kunzwisisa mikana yekukunda mumitambo yakasiyana-siyana nemabheti.
- Kuongorora Njodzi: Mubhizinesi nehutano hwevanhu, mukana wekuti njodzi iitike unoshandiswa kuongorora njodzi uye kuita sarudzo dziri nani.
- Kuenzanisa Mamiriro Ekunze: Mikana inobatsira vanoongorora mamiriro ekunze kufanotaura mukana wekuti mamiriro ekunze akasiyana-siyana aitike.
Mhedziso
Dzidziso yefungidziro inoita basa rakakosha muhuwandu, mudzidziso uye mukuita. Nekunzwisisa pfungwa dzakakosha uye misimboti mikuru yedzidziso yefungidziro yefungidziro, tinogona kuongorora data zvinobudirira, kufanotaura, uye kuita sarudzo dzakavakirwa paruzivo. Mashandisirwo edzidziso yefungidziro yefungidziro yefungidziro haagumiri mudzidzo yepamusoro kana kutsvagisa chete; anopinda muchikamu chese chehupenyu hwedu hwezuva nezuva. Zvechokwadi, pasina dzidziso yefungidziro yefungidziro yefungidziro, minda yakawanda yesainzi nemaindasitiri ingadai isina kukura kusvika payakasvika.
