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Random variables and expectation
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.
ຕົວຢ່າງທີ່ໄດ້ເຮັດ · 1 - (5/6)^4
Evaluate 1 - (5/6)^4
1 - \left(\frac{5}{6}\right)^{4}
ຂັ້ນຕອນຕໍ່ຂັ້ນຕອນ
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.
ເປີດເຜີຍຄຳຕອບ
\frac{671}{1296} \approx 0.51775
ປັດຈຸບັນທ່ານ
ເລືອກບັນຫາ ຫຼື ພິມ ຫຼື ແຕ້ມເອງ. ທຸກບາດກ້າວ, ຮູບ, ຄໍາຕອບຖືກລົບຈົນກວ່າເຈົ້າຈະຖາມມັນ.
ຮັກສາການເຮັດວຽກຂອງທ່ານໄວ້
ບັນຊີຟຣີ ເພີ່ມຂໍ້ມູນໃສ່ບົດຮຽນທຸກບົດ, ບັນທຶກຂອງສິ່ງທີ່ທ່ານໄດ້ເຮັດແລ້ວ, ບັນຫາທີ່ທ່ານໄດ້ແກ້ໄຂໄວ້ໃນບ່ອນດຽວ ແລະ ຄູສອນທີ່ທ່ານສາມາດຖາມກ່ຽວກັບໜ້ານີ້. ຄະນິດສາດເອງແມ່ນເປີດໃຫ້ທຸກຄົນ, ບໍ່ວ່າຈະໄດ້ເຂົ້າສູ່ລະບົບ ຫຼື ບໍ່.
ລົງທະບຽນ
ចូល
ຕົວສະແດງທີ່ໃຊ້ຢູ່ທີ່ນີ້
ກົດຕົວອັກສອນໃດໜຶ່ງເພື່ອເບິ່ງຄວາມໝາຍເຕັມ, ຮູບ ແລະ ຕົວອັກສອນແຕ່ລະຕົວໃນມັນໝາຍຄວາມວ່າແນວໃດ.
P(A) probability, conditional probability Chance of A; chance of A given that B happened. \approx approximately equal Equal to the precision shown, not exactly. \leq less/greater than or equal Inequalities that allow equality; < and > exclude it. n! factorial n × (n−1) × … × 1; the number of orderings of n things. 0! = 1. \binom{n}{k} binomial coefficient, "n choose k" Number of k-element subsets of n things: n!/(k!(n−k)!). \sum_{k=1}^{n} a_k summation Add a_k for k = 1 up to n. \int f(x) integral Antiderivative (indefinite) or signed area from a to b (definite). A \cup B union, intersection, difference In either; in both; in A but not B. \bar{x} sample mean, population mean Average of the data; average of the whole population. \sigma standard deviation, sample s.d., variance Typical distance from the mean; its square. E[X] expected value, variance Probability-weighted average of X; its spread. N(\mu normal distribution, z-score The bell curve with mean μ and variance σ²; (x − μ)/σ. \mu(A) measure of A Size of a set; the family of sets that can be measured.
ຕົວສະແດງໃນໜ້ານີ້
ກົດເພື່ອເບິ່ງຄວາມໝາຍຂອງມັນ
P(A) probability › \approx approximately equal › \leq less/greater than or equal › n! factorial › \binom{n}{k} binomial coefficient › \sum_{k=1}^{n} a_k summation › \int f(x) integral › A \cup B union › \bar{x} sample mean › \sigma standard deviation › E[X] expected value › N(\mu normal distribution › \mu(A) measure of A ›
ວິທີການ: Sample spaces and the axioms
Power: (5/6)^4 = 625/1296. Simplify.
ຄໍາຖາມທີ່ຄົນຖາມ
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.
ເພີ່ມເຕີມໃນ Probability Theory
Random variables and expectation The common distributions The law of large numbers and the central limit theorem