Random experiment
Summary
A random experiment is a procedure that we can repeat as often as we like and that has a well-defined set of possible results. The set of these results is the sample space of the experiment. The experiment is random when it has more than one possible result, and deterministic when it has exactly one.
Remarks
Each repetition of the experiment is a trial. Each trial gives exactly one outcome. A toss of a coin and a roll of a die are random experiments.
Explanations
L1 human
A random experiment is an action whose result you cannot predict, but whose possible results you know in advance. When you roll a die, you do not know the number that you will get, but you know that it is one of .
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- Variance 007QED3E0Y
- Prior probability 00NBBSXRQS
- Event 00SQGJNRTB
- Chernoff bound 014PEBGDYF
- Chapman–Kolmogorov equation 01APZ8GDQH
- Bias of an estimator 01BD2TFFP4
- Identically distributed random variables 01X8YSDTBW
- Law of the unconscious statistician 01ZWX875AT
- Density of the normal distribution 027JF1FBB0
- Exponential distribution 028Z8WC5Y9
- Covariance matrix 02CBHV4ZZQ
- Chebyshev's inequality 02HZ1BK3MW
- Characteristic function of a sum of independent random variables 02JGYG0T7M
- Stationary distribution 02KYGSCTCN
- Bernoulli process 02XPXR1FBK
- Markov chain 033TJBZDG0
- Statistic 036756NFD6
- Law of total variance 03BY5XTNA4
- Variance of the normal distribution 03EESZDB9A
- Cauchy–Schwarz inequality for expectations 03PGHKAJG3
- Monotonicity of probability 0464Z0JP2E
- Correlation coefficient 04CTY6XYWN
- Variance under translation 04CYN5G6RY
- Almost sure convergence 04P7D63W8P
- Law of total expectation 04RRB6HM00
- Probability density function 04YG690N5V
- Expectation of a product of independent random variables 05AW1G0WE1
- Likelihood function 05FSTXM92W
- Markov's inequality 05PWWHYBX5
- Standard score 05RZ4YZG4E
- Poisson point process 05TG0SE4HT
- Gamma distribution 06395GBNWD
- De Moivre–Laplace theorem 065X9S8CM3
- Buffon's needle problem 06X5PF6YFP
- Kolmogorov's zero–one law 073Q8Z94KG
- Independent random variables are uncorrelated 077GN9HDR6
- Convolution of probability distributions 07CHJ5YX28
- Normal distribution 07RXBVTVZB
- Mean of the Poisson distribution 086HEVXR9Z
- Statistical hypothesis test 087P03NEND
- Independence means the joint law is the product of the marginals 08QCA2F1NX
- Median 08W2CW8PKW
- Geometric probability 0924BCD257
- Dirac measure 099SXAG014
- Method of moments 09J1H07VAH
- Mean of the normal distribution 09PR1V6RWR
- Independent sigma-algebras 09T8ZHST1V
- Independent and identically distributed random variables 0AJN7WHBJZ
- Classical definition of probability 0AKNPYQ04R
- Pairwise independent events that are not mutually independent 0AR4B3K5QD
- Marginal distribution 0AXP2Z5N9H
- Moment-generating function of the normal distribution 0B1G4E21G7
- Quantile function 0B3Q3XDM5X
- Weak law of large numbers 0BFDHF2H7N
- Multiplication rule 0BS3RMX8HM
- Addition rule for two events 0BZQ6ZX584
- Random walk 0C08YMV95H
- Random variable with a density 0C21RZG5V2
- Uncorrelated random variables that are not independent 0C6J8BQXVR
- Kurtosis 0CBQVVNBMP
- Martingale 0CDVK9RQBH
- Variance of a sum 0D86GJEZ39
- Probability axioms 0DAX8PMAJ4
- Mean of the geometric distribution 0DB0R4N5XX
- Expected value 0DCT0QZVQ1
- Strong law of large numbers 0DFWHQ839T
- Covariance 0DJ8W3HP2D
- Random variable 0DKRR22AEQ
- Base rate fallacy 0E44JMG6NV
- Law of total probability 0E5G5FMT2R
- Independence of two random variables 0E9502NT92
- Neyman–Pearson lemma 0EE19CFEEF
- Convergence in probability 0EFDDXTVD6
- Boole's inequality 0EGSEE9J9R
- P-value 0EHYZFZ4PK
- Chi-squared test 0EN0V3NY20
- Convergence in probability implies convergence in distribution 0EPTDZPJ83
- Central limit theorem 0EPZC4Z1FC
- 68–95–99.7 rule 0EYQ03XCR3
- Transition matrix 0F1KBVY161
- Conditional variance 0F1SN93KXE
- Conditional probability 0FJB06AD2P
- Lévy's continuity theorem 0FPWF7TTMB
- Convergence of random variables 0FQ968YKA1
- Maximum likelihood estimation 0FREPFKNS7
- Multivariate normal distribution 0G558GJQMW
- Mutual independence of events 0GCVEV6BJA
- Skewness 0GQ3H7VW3V
- Galton–Watson process 0H631CZP5K
- Markov property 0HB8SXHPFA
- Student's t-test 0HYP606RYF
- Discrete random variable 0J6Z6H5VQJ
- Bernoulli distribution 0J97P5KZY0
- Convergence in distribution 0JDAQHWA9N
- The cumulative distribution function determines the distribution 0JEVZAFDY6
- Sample variance 0JN9P4A944
- Bayesian inference 0JWRJX2RMP
- Confidence interval 0K4NMMJBG2
- Posterior probability 0KJ7ZS8AJA
- Variance under scaling 0KVQ9D86BM
- Discrete uniform distribution 0KYP951QWH
- Coupon collector's problem 0MXCP7MXWJ
- Cumulative distribution function 0MXMS3AE13
- Characteristic function 0MYDNRT7PP
- Pairwise independence 0N57D1XY6T
- Cauchy distribution 0NA6Q82YR7
- Bayes' theorem 0NM6E9VW04
- Variance as the mean of the square minus the square of the mean 0NMF95YK8W
- Birthday problem 0NMWG2PHJ0
- Moment-generating function 0NNRNGKMFM
- Student's t-distribution 0NQ5798SB1
- Characteristic function of the normal distribution 0NS0TDA4E2
- Second Borel–Cantelli lemma 0NWXRAMEE7
- Sum of independent normal random variables 0NXGPJWNFN
- Independence of two events 0P0MZ4X682
- Linearity of expectation 0P7PTC8DDE
- Monty Hall problem 0PBWWQD9KY
- Moment 0PH0VHTQS0
- Bernoulli trial 0PHC9FE2V5
- Beta distribution 0PP5ZAJPP7
- Probability of the complement 0PQEBTYDZM
- Expectation with respect to the binomial distribution 0PVCTCKD3C
- Cumulant generating function 0Q2QC81VTW
- Joint probability distribution 0QAR0XDZH4
- Probability distribution 0QB913WM5E
- Stochastic process 0QH5ENKZM1
- Sample mean 0QNRBHWV35
- Type I and type II errors 0R41PVFA39
- Almost surely 0R46A1XY60
- Generating function of a sum of independent random variables 0REMT01N36
- Chi-squared distribution 0RFMMBHFTV
- Limit of the cumulative distribution function at infinity 0RJ5TZH6G0
- Hypergeometric distribution 0SPBPW3K61
- Moments are derivatives of the moment-generating function at zero 0STK8KEY9G
- Almost sure convergence implies convergence in probability 0SVN6X695K
- Bertrand paradox 0T0JWJ3M47
- First Borel–Cantelli lemma 0T6WS7TT77
- The characteristic function determines the distribution 0T8BYAFEXX
- Law of a random variable 0TST4MHA3A
- Convergence in mean 0TTA57SEJG
- Estimator 0TTNRP5PFQ
- Variance of a sum of independent random variables 0V0778DCW9
- Mean squared error 0V4VSCBXP3
- Poisson distribution 0VEFSSKX18
- Probability measure 0VGMEBVW1M
- Binomial distribution 0VRWZDWW6B
- Standard deviation 0VTN5RKNC5
- Law of total probability for an event and its complement 0W62TKMW7V
- Sample space 0W7NFW23RF
- Probability mass function 0WF4EJP91W
- Gambler's ruin 0WFMKK7DFZ
- Continuous uniform distribution 0WGDPYR30Q
- Hoeffding's inequality 0WPDNXGSSN
- Moment-generating function of a sum of independent random variables 0WRZ170YEH
- Continuity of probability measures 0X8HBKCSYB
- Independence of random variables 0XCE070V8B
- Geometric distribution 0XCVV5Q500
- Monotonicity of the cumulative distribution function 0XD22PBMWA
- Consistent estimator 0XJVF81QF6
- Poisson limit theorem 0XKTZRWTXX
- Negative binomial distribution 0XN7KEVSSS
- Outcome 0Y5R7TPNT1
- Tail sum formula for expectation 0Y6QNF1J49
- Conditional expectation 0YAMJRK04E
- Absorbing Markov chain 0YB93GWTKK
- Sum of independent Poisson random variables 0YH1M56SBN
- Conditional probability distribution 0YVDC5PYDW
- Probability-generating function 0Z8PSSAVBA
- Memorylessness 0ZAZZ34WQS
- Conditional independence 0ZJ87ZZ8PK
- Central moment 0ZT24EC90K
- Law of large numbers 0ZVEAYVRC3
- Probability space 0ZYBZ34RT2
Sources
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- Bernoulli trial 0PHC9FE2V5
- Sample space 0W7NFW23RF