e y formula

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e y formula Formula for these things and quick examples on how to use them

The conditional expectation also called the conditional mean or conditional expected value is simply the mean calculated after a set of prior conditions has happened Put more formally the conditional expectation E X Y of a random variable is that variable s expected value calculated with respect to its conditional probability E X Y is the expectation of a random variable the expectation of X conditional on Y E X Y y on the other hand is a particular value the expected value of X when Y y

e y formula

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e y formula
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FORMULA
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Conditional Expectation as a Function of a Random Variable Remember that the conditional expectation of X given that Y y is given by E X Y y xi RXxiPX Y xi y Note that E X Y y depends on the value of y In other words by changing y E X Y y can also change 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

E X Y 1 3 0 3 2 3 0 1 1 6 0 1 2 6 0 5 The upper left cell of the table X 1 Y 3 X 1 Y 3 has a probability of 0 3 0 3 of occurring So this cell contributes 0 3 1 3 0 3 1 3 to the expectation of XY X Y The other cells are similar The covariance of X and Y is Cov X Y E XY E X E Y

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Var Y E Var Y X Var E Y X In words The marginal variance is the sum of the expected value of the conditional variance and the variance of the conditional means Euler s formula states that for any real number x one has where e is the base of the natural logarithm i is the imaginary unit and cos and sin are the trigonometric functions cosine and sine respectively This complex exponential function is sometimes denoted cis x cosine plus i sine

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e y formula - 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