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The proposition in probability theory known as the law of total expectation, [1] the law of iterated expectations [2] (LIE), Adam's law, [3] the tower rule, [4] and the smoothing theorem, [5] among other names, states that if is a random variable whose expected value is defined, and is any random variable on the same probability space, then
The law of total expectation and the law of total variance generalize naturally to conditional cumulants. ... In the above moment-cumulant formula\ ...
The term law of total probability is sometimes taken to mean the law of alternatives, which is a special case of the law of total probability applying to discrete random variables. [ citation needed ] One author uses the terminology of the "Rule of Average Conditional Probabilities", [ 4 ] while another refers to it as the "continuous law of ...
In probability theory, the law of total variance [1] or variance decomposition formula or conditional variance formulas or law of iterated variances also known as Eve's law, [2] states that if and are random variables on the same probability space, and the variance of is finite, then
This formula also holds in multidimensional case ... Law of total expectation – the expected value of the conditional expected value of X given Y is the same as the ...
Toy Shop: 1937. Although, we're not sure which story this is, it's clearly one filled with lots and lots of toys. Here, a little girl lovingly points to a baby doll in a window.
From planetary meet-ups to the first total lunar eclipse in three years, here are the top astronomy events to look for throughout 2025: Stellar views of Mars will greet stargazers in January as ...
Expectation (or mean), variance and covariance. Jensen's inequality; General moments about the mean; Correlated and uncorrelated random variables; Conditional expectation: law of total expectation, law of total variance; Fatou's lemma and the monotone and dominated convergence theorems; Markov's inequality and Chebyshev's inequality