Math 2.0

Subjects

60 Probability theory and stochastic processes

See MSC 60 on zbMATH Open.

NameTagKindMSC
Mutual independence of events001B78R0DJconcept60A05
Variance007QED3E0Ydefinition60A05
Independent and identically distributed random variables00MRN0FARVconcept60A05
Event00SQGJNRTBdefinition60A05
Chernoff bound014PEBGDYFstatement60E15
Chapman–Kolmogorov equation01APZ8GDQHstatement60J10
Law of a random variable01EQPZ6RYZconcept60E05
Identically distributed random variables01X8YSDTBWdefinition60E05
Moment01XAHPADBAconcept60E05
Law of the unconscious statistician01ZWX875ATstatement60A05
Density of the normal distribution027JF1FBB0definition60E05
Exponential distribution028Z8WC5Y9definition60E05
Chebyshev's inequality02HZ1BK3MWstatement60E15
Characteristic function of a sum of independent random variables02JGYG0T7Mstatement60E10
Stationary distribution02KYGSCTCNdefinition60J10
Discrete uniform distribution02MY6WZXEQconcept60E05
Bernoulli process02XPXR1FBKdefinition60G50
Event031TPJVS74concept60A05
Markov chain033TJBZDG0definition60J10
Bernoulli distribution0386Y0Z7Y7concept60E05
Independence of two events03AHF0XRVGconcept60A05
Absorbing Markov chain03AN9X29R7concept60J10
Law of total variance03BY5XTNA4statement60A10
Variance of the normal distribution03EESZDB9Astatement60E05
Cauchy–Schwarz inequality for expectations03PGHKAJG3statement60E15
Random variable with a density045D8P03E0concept60E05
Monotonicity of probability0464Z0JP2Estatement60A05
Variance0477R9PYAEconcept60A05
Variance under translation04CYN5G6RYstatement60A05
Geometric distribution04P2SR252Nconcept60E05
Almost sure convergence04P7D63W8Pdefinition60F15
Law of total expectation04RRB6HM00statement60A10
Random walk04VZE3FZXFconcept60G50
Probability density function04YG690N5Vdefinition60E05
Classical definition of probability051CYS71H5concept60A05
Probability measure059TJN0NZ1concept60A10
Normal distribution05AQE0QR0Dconcept60E05
Expectation of a product of independent random variables05AW1G0WE1statement60A05
Markov's inequality05PWWHYBX5statement60E15
Poisson point process05TG0SE4HTdefinition60G55
Gamma distribution06395GBNWDdefinition60E05
De Moivre–Laplace theorem065X9S8CM3statement60F05
Buffon's needle problem06X5PF6YFPproblem60D05
Kolmogorov's zero–one law073Q8Z94KGstatement60F20
Independent random variables are uncorrelated077GN9HDR6statement60A05
Convolution of probability distributions07CHJ5YX28definition60E05
Normal distribution07RXBVTVZBdefinition60E05
Median07Y2E7P9NPconcept60E05
Mean of the Poisson distribution086HEVXR9Zstatement60E05
Independence means the joint law is the product of the marginals08QCA2F1NXstatement60A05
Median08W2CW8PKWdefinition60E05
Identically distributed random variables08ZDW5SA3Bconcept60E05
Geometric probability0924BCD257concept60D05
Central moment09753QQDCKconcept60E05
Conditional probability0990W5PN13concept60A05
Mean of the normal distribution09PR1V6RWRstatement60E05
Student's t-distribution09RTQRK5PCconcept60E05, 62E15
Independent sigma-algebras09T8ZHST1Vdefinition60A05
Convergence in mean0A2HNZC44Kconcept60F25
Chi-squared distribution0A9EB0KQBCconcept60E05, 62E15
Almost sure convergence0AAXWGT5TDconcept60F15
Independent and identically distributed random variables0AJN7WHBJZdefinition60A05
Classical definition of probability0AKNPYQ04Rdefinition60A05
Pairwise independent events that are not mutually independent0AR4B3K5QDcounterexample60A05
Continuous uniform distribution0AREFQ9Z65concept60E05
Moment-generating function of the normal distribution0B1G4E21G7statement60E10
Quantile function0B3Q3XDM5Xdefinition60E05
Independent sigma-algebras0B5BA4FRWSconcept60A05
Markov property0B77KZCQ51concept60J05, 60J10
Gamma distribution0B80PAQD3Cconcept60E05
Weak law of large numbers0BFDHF2H7Nstatement60F05
Multiplication rule0BS3RMX8HMstatement60A05
Addition rule for two events0BZQ6ZX584statement60A05
Random walk0C08YMV95Hdefinition60G50
Density of the normal distribution0C12P4W4RHconcept60E05
Random variable with a density0C21RZG5V2definition60E05
Uncorrelated random variables that are not independent0C6J8BQXVRcounterexample60A05
Martingale0CDVK9RQBHdefinition60G42
Bernoulli process0CQQG3DEW9concept60G50
Martingale0D0GBNDKDHconcept60G42
Probability mass function0D6J4B671Dconcept60E05
Variance of a sum0D86GJEZ39statement60A05
Probability axioms0DAX8PMAJ4concept60A05
Mean of the geometric distribution0DB0R4N5XXstatement60E05
Expected value0DCT0QZVQ1definition60A05
Strong law of large numbers0DFWHQ839Tstatement60F15
Covariance0DJ8W3HP2Ddefinition60A05
Random variable0DKRR22AEQdefinition60A05
Probability distribution0DVDCMA2DKconcept60E05
Law of total probability0E5G5FMT2Rstatement60A05
Independence of two random variables0E9502NT92definition60A05
Exponential distribution0E99F51GVBconcept60E05
Probability-generating function0EBCWQ8BVEconcept60E05
Convergence in probability0EFDDXTVD6definition60F05
Boole's inequality0EGSEE9J9Rstatement60E15
Convergence in probability implies convergence in distribution0EPTDZPJ83statement60F05
Central limit theorem0EPZC4Z1FCstatement60F05
Beta distribution0EW824Z7G2concept60E05
68–95–99.7 rule0EYQ03XCR3example60E05
Transition matrix0F1KBVY161definition60J10
Conditional variance0F1SN93KXEdefinition60A10
Transition matrix0F462493EAconcept60J10
Outcome0F50N2P3FCconcept60A05
Convolution of probability distributions0F8GDKM0A7concept60E05
Conditional probability0FJB06AD2Pdefinition60A05
Lévy's continuity theorem0FPWF7TTMBstatement60E10, 60F05
Convergence of random variables0FQ968YKA1concept60F05, 60F15
Galton–Watson process0G1022YXVQconcept60J80
Markov chain0G48PYM96Qconcept60J10
Independence of two random variables0GBJACNAP6concept60A05
Mutual independence of events0GCVEV6BJAdefinition60A05
Cauchy distribution0GPG24Q3GRconcept60E05
Independence of random variables0GQ938GDE0concept60A05
Galton–Watson process0H631CZP5Kdefinition60J80
Cumulative distribution function0H8H7ZTHW2concept60E05
Markov property0HB8SXHPFAdefinition60J05
Random experiment0HM05N3FJDconcept60A05
Discrete random variable0J6Z6H5VQJdefinition60E05
Bernoulli distribution0J97P5KZY0definition60E05
Convergence in distribution0JDAQHWA9Ndefinition60F05
The cumulative distribution function determines the distribution0JEVZAFDY6statement60E05
Covariance0KBFAWYRTEconcept60A05
Stationary distribution0KRH5157WPconcept60J10
Variance under scaling0KVQ9D86BMstatement60A05
Discrete uniform distribution0KYP951QWHdefinition60E05
Poisson point process0MTNR28K60concept60G55
Coupon collector's problem0MXCP7MXWJproblem60C05
Cumulative distribution function0MXMS3AE13definition60E05
Characteristic function0MYDNRT7PPdefinition60E10
Cumulant generating function0N2SP6K9ZCconcept60E10
Pairwise independence0N57D1XY6Tdefinition60A05
Cauchy distribution0NA6Q82YR7definition60E05
Probability space0NFPJVJJHXconcept60A05
Variance as the mean of the square minus the square of the mean0NMF95YK8Wstatement60A05
Birthday problem0NMWG2PHJ0example60C05
Moment-generating function0NNRNGKMFMdefinition60E10
Student's t-distribution0NQ5798SB1definition60E05, 62E15
Characteristic function of the normal distribution0NS0TDA4E2statement60E10
Second Borel–Cantelli lemma0NWXRAMEE7statement60F20
Sum of independent normal random variables0NXGPJWNFNstatement60E05
Independence of two events0P0MZ4X682definition60A05
Standard deviation0P4FTHHMYSconcept60A05
Linearity of expectation0P7PTC8DDEstatement60A05
Monty Hall problem0PBWWQD9KYproblem60C05
Moment0PH0VHTQS0definition60E05
Bernoulli trial0PHC9FE2V5concept60A05
Random variable0PNRKMRC55concept60A05
Beta distribution0PP5ZAJPP7definition60E05
Probability of the complement0PQEBTYDZMstatement60A05
Expectation with respect to the binomial distribution0PVCTCKD3Cstatement60E05
Cumulant generating function0Q2QC81VTWdefinition60E10
Convergence in probability0QA1HBD9Z4concept60F05
Probability distribution0QB913WM5Edefinition60E05
Stochastic process0QH5ENKZM1concept60G05
Almost surely0R46A1XY60definition60A05
Generating function of a sum of independent random variables0REMT01N36statement60E05
Chi-squared distribution0RFMMBHFTVdefinition60E05, 62E15
Limit of the cumulative distribution function at infinity0RJ5TZH6G0statement60E05
Probability theory0RWE7CPJ32concept60A05
Hypergeometric distribution0SPBPW3K61definition60E05
Convergence in distribution0SRYJGXKR4concept60F05
Almost surely0ST21PGDAPconcept60A05
Moments are derivatives of the moment-generating function at zero0STK8KEY9Gstatement60E10
Almost sure convergence implies convergence in probability0SVN6X695Kstatement60F15
Sample space0SWXJHKJ02concept60A05
Bertrand paradox0T0JWJ3M47example60D05
First Borel–Cantelli lemma0T6WS7TT77statement60F20
The characteristic function determines the distribution0T8BYAFEXXstatement60E10
Conditional independence0THJ7416DXconcept60A05
Law of a random variable0TST4MHA3Adefinition60E05
Convergence in mean0TTA57SEJGdefinition60F25
Conditional expectation0TTDGTEFMNconcept60A10
Variance of a sum of independent random variables0V0778DCW9statement60A05
Characteristic function0V5B6D6BQHconcept60E10
Poisson distribution0VEFSSKX18definition60E05
Probability measure0VGMEBVW1Mdefinition60A10
Conditional variance0VGPX25NXQconcept60A10
Binomial distribution0VRWZDWW6Bdefinition60E05
Standard deviation0VTN5RKNC5definition60A05
Law of total probability for an event and its complement0W62TKMW7Vstatement60A05
Sample space0W7NFW23RFdefinition60A05
Binomial distribution0WCWA1KT3Mconcept60E05
Probability mass function0WF4EJP91Wdefinition60E05
Gambler's ruin0WFMKK7DFZproblem60G50, 60G40
Continuous uniform distribution0WGDPYR30Qdefinition60E05
Hoeffding's inequality0WPDNXGSSNstatement60E15
Expected value0WQNRCNY3Mconcept60A05
Moment-generating function0WQVXP7PDBconcept60E10
Moment-generating function of a sum of independent random variables0WRZ170YEHstatement60E10
Discrete random variable0X2J0VY6DNconcept60E05
Hypergeometric distribution0X3Y0ZSKNFconcept60E05
Quantile function0X60VE98HNconcept60E05
Continuity of probability measures0X8HBKCSYBstatement60A10
Poisson distribution0XB9GQTN9Gconcept60E05
Negative binomial distribution0XBRG3965Fconcept60E05
Independence of random variables0XCE070V8Bdefinition60A05
Geometric distribution0XCVV5Q500definition60E05
Monotonicity of the cumulative distribution function0XD22PBMWAstatement60E05
Poisson limit theorem0XKTZRWTXXstatement60F05
Negative binomial distribution0XN7KEVSSSdefinition60E05
Outcome0Y5R7TPNT1definition60A05
Tail sum formula for expectation0Y6QNF1J49statement60A05
Conditional expectation0YAMJRK04Edefinition60A10
Absorbing Markov chain0YB93GWTKKdefinition60J10
Sum of independent Poisson random variables0YH1M56SBNstatement60E05
Conditional probability distribution0YVDC5PYDWdefinition60E05
Probability-generating function0Z8PSSAVBAdefinition60E05
Memorylessness0ZAZZ34WQSconcept60E05
Pairwise independence0ZB3M68NYQconcept60A05
Conditional independence0ZJ87ZZ8PKdefinition60A05
Conditional probability distribution0ZN9EZTEM6concept60E05
Central moment0ZT24EC90Kdefinition60E05
Law of large numbers0ZVEAYVRC3concept60F05, 60F15
Probability density function0ZY9DX8FBFconcept60E05
Probability space0ZYBZ34RT2definition60A05