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Any definition of expected value may be extended to define an expected value of a multidimensional random variable, i.e. a random vector X. It is defined component by component, as E[X] i = E[X i]. Similarly, one may define the expected value of a random matrix X with components X ij by E[X] ij = E[X ij].
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 ...
Step 7 states that the expected value in B = 1/2(2A + A/2). It is pointed out that the 'A' in the first part of the formula is the expected value, given that envelope A contains less than envelope B, but the 'A', in the second part of the formula is the expected value in A, given that envelope A contains more than envelope B.
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
In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought ...
The departure of the upper tail of the distribution from the expected trend along the diagonal is due to the presence of substantially more large test statistic values than would be expected if all null hypotheses were true. The red point corresponds to the fourth largest observed test statistic, which is 3.13, versus an expected value of 2.06.
In statistics, expected mean squares (EMS) are the expected values of certain statistics arising in partitions of sums of squares in the analysis of variance (ANOVA). They can be used for ascertaining which statistic should appear in the denominator in an F-test for testing a null hypothesis that a particular effect is absent.
Cost := Value_per_minute_at_home * Time_I_leave_home + (If Time_I_leave_home < Time_from_home_to_gate Then Loss_if_miss_the_plane Else 0) The following graph displays the expected value taking uncertainty into account (the smooth blue curve) to the expected utility ignoring uncertainty, graphed as a function of the decision variable.
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