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Probability and Statistics
Probability and Statistics
foundations +18 more results +34 more equations +2 more depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) step_from (declared) step_from (declared) step_from (declared) step_from (declared) step_from (declared) step_from (declared) step_from (declared) step_from (declared) definition 11.1: Discrete probability space 11.1 Discrete probabi… definition 11.3: Discrete random variable 11.3 Discrete random… definition 11.4: Expectation 11.4 Expectation definition 11.6: Moments, variance, standard deviation 11.6 Moments, varianc… definition 11.8: Quantiles and median 11.8 Quantiles and me… definition 11.11: Covariance and correlation 11.11 Covariance and c… definition 11.13: Independence 11.13 Independence definition 11.16: Sample mean, variance and correlation 11.16 Sample mean, var… definition 11.20: Density 11.20 Density definition 11.21: Distribution function 11.21 Distribution fun… definition 11.23: Expectation, moments and quantiles in the continuous
case 11.23 Expectation, mom… definition 11.25: Joint density and independence 11.25 Joint density an… definition 11.28: Gaussian distribution 11.28 Gaussian distrib… proposition 11.2: Elementary rules 11.2 Elementary rules proposition 11.5: Transfer, linearity, monotonicity 11.5 Transfer, linear… proposition 11.7: Variance identity 11.7 Variance identity proposition 11.10: What the mean and the median minimise 11.10 What the mean an… proposition 11.12: Bilinearity 11.12 Bilinearity proposition 11.14: Independence implies zero covariance; the converse
fails 11.14 Independence imp… corollary 11.15: Bounds on the correlation
coefficient 11.15 Bounds on the co… proposition 11.17: Sampling identities 11.17 Sampling identit… proposition 11.22: Properties of the distribution
function 11.22 Properties of th… proposition 11.24: The algebra of the discrete case transfers 11.24 The algebra of t… proposition 11.26: Product rule 11.26 Product rule proposition 11.27: Probability integral transform 11.27 Probability inte… proposition 11.29: Gaussian moments 11.29 Gaussian moments equation 11.30: eq:prob-taylor eq. (11.30) equation 11.31: eq:prob-expbound eq. (11.31) equation 11.32: eq:prob-taylor-truncate eq. (11.32) equation 11.34: eq:prob-clt-product eq. (11.34) equation 11.35: eq:prob-clt-expansion eq. (11.35) equation 11.36: eq:prob-product-lemma eq. (11.36) equation 11.37: eq:prob-clt-limit eq. (11.37) equation 11.61: eq:prob-consistency-expansion eq. (11.61) equation 11.62: eq:prob-consistency-radius eq. (11.62) equation 11.63: eq:prob-consistency-negative eq. (11.63) equation 11.82: eq:prob-wilks-expansion eq. (11.82) equation 11.83: eq:prob-wilks-q eq. (11.83) equation 11.86: eq:prob-chernoff eq. (11.86) The chain of Probability and Statistics: 39 of 93 objects, read left to right from what the chapter assumes to what tests it. Solid lines are declared logical edges, dashed ones were inferred from the structure of the source. Click any node to open its own chain.