Summary This chapter contains sections titled: Expectation of a Random Variable Properties of Expectation Independent Random Variables Variance of a Random Variable Correlation Coefficient Properties of Normal
E(Y |X) is our best predictor of Y based on X. Best means it is the function of X with the lowest mean squared error (expected squared di↵erence between Y and prediction of Y ). It is called the Minimum Mean Square Estimate (MMSE) Theorem Let X, Y bejointly Normal random vari...
Expected value or expectation of a random variableXis defined, if it exists, in a mathematically precise way with respect to a probability space, typically denoted as(Ω,A,P), whereΩis the universe of possibilities,Athe set of possible events (which are the possible values of the random va...
In probability and statistics, the expectation or expected value, is the weighted average value of a random variable.
1 . The weight ofexpectationwas getting to them. 他们逐渐感觉到了期望带来的压力。 来自柯林斯例句 2 . We are confident in ourexpectationof a full recovery. 我们满怀信心地期待着完全康复。 来自《权威词典》 3 . The plaintiff is aged 30 and has a normalexpectationof life. ...
Thus, we can think of g(y)=E[X|Y=y]g(y)=E[X|Y=y] as a function of the value of random variable YY. We then write g(Y)=E[X|Y].g(Y)=E[X|Y]. We use this notation to indicate that E[X|Y]E[X|Y] is a random variable whose value equals g(y)=E[X|Y=y]g(y...
− σx2 2 , (1) where ϕx is the fixed intercept representing initial degradation, βx ∼ N (µx1, σx21) is a normal random variable, θx is a lognormal random variable that follows ln θx ∼ N (µx0, σx20), and εx(t) ∼ N (0, σx2) is a normal distrib...
Definition 1: If a discrete random variablexhas frequency functionf(x) then theexpected valueof the functiong(x) is defined as The equivalent for a continuous random variablexis wheref(x) is the probability density function.This is the total area between the curve of the functionh(x) and...
It is important to remember that participants received no feedback on their performance after the training period; however, they could (non-consciously or consciously) evaluate their performance by comparing the number of sensed heartbeats to their knowledge of the normal range of the resting HR (...
The conditional mean uses information from the previous period and is in general a random variable, depending on the information set Ft−1 and is given by: (1.5)mt≡E[yt|Ft−1]≡Et−1[yt], where yt is the rate of return of a particular stock or market portfolio from time t...