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- Law_of_total_expectation abstract "The proposition in probability theory known as the law of total expectation, the law of iterated expectations, the tower rule, the smoothing theorem, among other names, states that if X is an integrable random variable (i.e., a random variable satisfying E( | X | ) < ∞) and Y is any random variable, not necessarily integrable, on the same probability space, theni.e., the expected value of the conditional expected value of X given Y is the same as the expected value of X.(The conditional expected value E( X | Y ) is a random variable in its own right, whose value depends on the value of Y. Notice that the conditional expected value of X given the event Y = y is a function of y (this is where adherence to the conventional, rigidly case-sensitive notation of probability theory becomes important!). If we write E( X | Y = y) = g(y) then the random variable E( X | Y ) is just g(Y).One special case states that if is a partition of the whole outcome space, i.e. these events are mutually exclusive and exhaustive, then".
- Law_of_total_expectation wikiPageExternalLink ProbNotes.pdf,.
- Law_of_total_expectation wikiPageID "312397".
- Law_of_total_expectation wikiPageRevisionID "606505528".
- Law_of_total_expectation hasPhotoCollection Law_of_total_expectation.
- Law_of_total_expectation subject Category:Algebra_of_random_variables.
- Law_of_total_expectation subject Category:Statistical_laws.
- Law_of_total_expectation subject Category:Theory_of_probability_distributions.
- Law_of_total_expectation type Abstraction100002137.
- Law_of_total_expectation type Collection107951464.
- Law_of_total_expectation type Group100031264.
- Law_of_total_expectation type Law108441203.
- Law_of_total_expectation type StatisticalLaws.
- Law_of_total_expectation comment "The proposition in probability theory known as the law of total expectation, the law of iterated expectations, the tower rule, the smoothing theorem, among other names, states that if X is an integrable random variable (i.e., a random variable satisfying E( | X | ) < ∞) and Y is any random variable, not necessarily integrable, on the same probability space, theni.e., the expected value of the conditional expected value of X given Y is the same as the expected value of X.(The conditional expected value E( X | Y ) is a random variable in its own right, whose value depends on the value of Y. ".
- Law_of_total_expectation label "Law of total expectation".
- Law_of_total_expectation label "Legge delle aspettative iterate".
- Law_of_total_expectation label "全期望公式".
- Law_of_total_expectation sameAs Legge_delle_aspettative_iterate.
- Law_of_total_expectation sameAs m.01tc2v.
- Law_of_total_expectation sameAs Q2247110.
- Law_of_total_expectation sameAs Q2247110.
- Law_of_total_expectation sameAs Law_of_total_expectation.
- Law_of_total_expectation wasDerivedFrom Law_of_total_expectation?oldid=606505528.
- Law_of_total_expectation isPrimaryTopicOf Law_of_total_expectation.