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In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a subset of ...
To do this, instead of computing the conditional probability of failure, the algorithm computes the conditional expectation of Q and proceeds accordingly: at each interior node, there is some child whose conditional expectation is at most (at least) the node's conditional expectation; the algorithm moves from the current node to such a child ...
Conditional probabilities, conditional expectations, and conditional probability distributions are treated on three levels: discrete probabilities, probability density functions, and measure theory. Conditioning leads to a non-random result if the condition is completely specified; otherwise, if the condition is left random, the result of ...
An expectation of a random variable with respect to a regular conditional probability is equal to its conditional expectation. ... be shown with a counter-example:
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
For example, the conditional probability that someone unwell (sick) is coughing might be 75%, in which case we would have that P(Cough) = 5% and P(Cough|Sick) = 75 %. Although there is a relationship between A and B in this example, such a relationship or dependence between A and B is not necessary, nor do they have to occur simultaneously.
In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values. Stopped Brownian motion is an example of a martingale. It can model an even coin-toss ...
In this case, the covariance is the expectation of the product, and and are uncorrelated if and only if [] =. If and are independent, with finite second moments, then they are uncorrelated. However, not all uncorrelated variables are independent.