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Sample spaces and the axioms
Kolmogorov's axioms, events as sets, conditional probability and Bayes.
Probability is a measure on events: non-negative, total 1, additive over disjoint events. Conditional probability P(A|B) = P(A ∩ B)/P(B), and Bayes reverses the conditioning. Picture it: a tree diagram; multiply along branches, add across leaves. Think it: the axioms are measure theory with total mass 1, which is why the two subjects merged.
tusaale · 1 - (5/6)^4
tallaabo tallaabo
- 1 - \left(\frac{5}{6}\right)^{4} = 1 - \frac{625}{1296}
Power: (5/6)^4 = 625/1296.
- 1 - \frac{625}{1296} = \frac{671}{1296}
Simplify.
Jawaabta muuji
Haddaad Dooro dhibaato, ama qoraal ama sawirkaaga. Talaab kasta, sawir, jawaabta qarsoon ilaa aad weydiiso.
A xisaab bilaash ah oo ku daray qoraalada waxbarasho kasta, diiwaanka waxa aad dhamaatay, dhibaatooyinka aad xal u tahay meel kaliya, iyo macallinka aad weydiisan kartaa oo ku saabsan bogga. Xisaabta oo keliya waa u furan yahay qof kasta, la diiwaan geliyey ama aan.
Ku soo biir Ku soo galCalaamadaha la isticmaalay halkan
Taab calaamad kasta oo loogu talagalay qeexidda buuxda, sawir, iyo waxa xarfaha oo dhan ka mid ah ka dhigan tahay.
Sida loo: Sample spaces and the axioms
- Power: (5/6)^4 = 625/1296.
- Simplify.
Su'aalaha dadku waydiiyaan
What is the difference between probability and statistics?
Probability goes from a known model to what the data should look like; statistics goes from data back to the model. Probability theory is the deductive half.
What does the law of large numbers promise?
That the average of many independent samples converges to the expected value. It says nothing about any single trial.
In ka badan Probability Theory
Random variables and expectationThe common distributionsThe law of large numbers and the central limit theorem