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Since the probabilities must satisfy p 1 + ⋅⋅⋅ + p k = 1, it is natural to interpret E[X] as a weighted average of the x i values, with weights given by their probabilities p i. In the special case that all possible outcomes are equiprobable (that is, p 1 = ⋅⋅⋅ = p k), the weighted average is given by the standard average. In the ...
The conditional expectation of rainfall for an otherwise unspecified day known to be (conditional on being) in the month of March, is the average of daily rainfall over all 310 days of the ten–year period that fall in March. Similarly, the conditional expectation of rainfall conditional on days dated March 2 is the average of the rainfall ...
In statistics, kernel regression is a non-parametric technique to estimate the conditional expectation of a random variable.The objective is to find a non-linear relation between a pair of random variables X and Y.
The expected value of a random variable is the weighted average of the possible values it might take on, with the weights being the respective probabilities. More generally, the expected value of a function of a random variable is the probability-weighted average of the values the function takes on for each possible value of the random variable.
Then the first, "unexplained" term on the right-hand side of the above formula is the weighted average of the variances, hσ h 2 + (1 − h)σ t 2, and the second, "explained" term is the variance of the distribution that gives μ h with probability h and gives μ t with probability 1 − h.
The summation can be interpreted as a weighted average, and consequently the marginal probability, (), is sometimes called "average probability"; [2] "overall probability" is sometimes used in less formal writings. [3] The law of total probability can also be stated for conditional probabilities:
However, the conditional probability P(A|B 1) = 1, P(A|B 2) = 0.12 ÷ (0.12 + 0.04) = 0.75, and P(A|B 3) = 0. On a tree diagram, branch probabilities are conditional on the event associated with the parent node. (Here, the overbars indicate that the event does not occur.) Venn Pie Chart describing conditional probabilities
The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others.