Given a random variable, we often compute the expectation and variance, two important summary statistics. The expectation describes the average value and the variance describes the spread (amount of variability) around the expectation.Definition 2.3.1. The expectation of an RV XX is the real ...
Let g(x) = E(Y |X = x). Then the conditional expectation of Y given X, denoted E(Y |X), is defined to be the random variable g(X). In other words, if after doing the experiment X crystallizes into x, then E(Y |X) crystallizes into g(x). 换言之,E(Y|X)事实上是一个关...
Theminimum mean squared error (MMSE)estimate of the random variableXX, given that we have observedY=yY=y, is given by x^M=E[X|Y=y].x^M=E[X|Y=y]. Example XX XX Y=yY=y Solution First we need to find the posterior density,fX|Y(x|y). We have ...
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...
Predictive coding theories suggest that core symptoms in autism spectrum disorders (ASD) may stem from atypical mechanisms of perceptual inference (i.e., inferring the hidden causes of sensations). Specifically, there would be an imbalance in the precisi
Artificial intelligence (AI) has been proven to be a disruptive financial technology in the context of mobile banking that can provide more practical value to users and banks. AI is a critical way of facilitating user acceptance and adoption of mobile ba
in the case of a particle in a 1-D box. The expected value of the particle's momentum is zero because it has equal probability of moving either to the left or to the right, however zero is not the most probable speed, as it will always have some momentum. Mathematically ...
Finally, in supplemental analyses, we evaluated the quadratic effects of expectations and aspirations (Fig.1B) and the aspirations-expectations gap (Fig.1B) to test Goldilocks Effects. The quadratic terms were the squared terms for aspirations and expectations after zero-mean centering these variable...
The search was assumed to have reached convergence (to a local optimum) when the mean squared error (MSE, smoothed using a moving median with a window size of 3) for the E-step varies by less than a user-specified tolerance (0.1% by default) for 3 consecutive iterations [72]. In ...
Methods: The initial scale consisted foremost of items from pre-existing measures with a few new items added. As suggested for smaller variable sets, we applied common factor analysis with squared multiple correlations as initial communality estimates for 3-7 factor models rotated according to ...